I transplant tomatoes in about 6 weeks. Much longer than that results in leggy plants. If the weather is still a bit nippy then, I would cover them over with a large container overnight if needed.

Lettuce could be set out before the last frost date ....so don't let them get stunted in the pots.

Welcome to growing your own produce - I've been doing it for 30 years and still have questions. I'm in Maine, so my climate is very different, but some basics still apply.

First of all, of the vegetables you list, tomatoes, lettuce, and cucumbers are the best candidates for early starting and transplanting, but in your climate the need to do so is far less than here where the season is too short to bring tomatoes to ripeness. There is no reason not to start early, but it is not necessary.
You likely started the lettuce too soon... typically it forms its first "true" leaves within two weeks, and is then ready to transplant, but that doesn't mean it must be. Provided there is enough root space, you can leave them in containers for quite some time. Additionally, while March 16th is your average last frost date, lettuce can be safely planted before that date with some minor preparation - it tolerates cool soil temps far better than tomatoes or cucumbers will... in fact, March 16th may well be too soon to plant those crops without applying some soil warming techniques.
Tomatoes actually can benefit from longer growing times before transplanting, again, with some added attention. Once the plants have formed their third set of leaves, you should remove the bottom pair and transplant into a deeper container, to the depth where the leaves once were. The plant will create new roots from the stem, and you will have a few more weeks growing time before you put them out in the garden. This is NOT true for most other plants, which typically should be planted at the same depth they were growing at before transplanting. With the tomatoes, the same procedure can be used when the plants are put in the garden, but rather than plant deeper, the stem is buried almost horizontally rather than vertically, with the leafy part bent upright. This keeps the root zone closer to the upper level of the soil, where the most nutrients are, and creates a strong anchor.
Finally, many new growers start way too many plants at the beginning of the season. You may have far too much iceberg in June and none in October. Be diligent in your planning. Don't depend on internet resources for the best information. Look in your library, extension office, and local schools and organizations for more appropriate local expertise. Good authors too look for are Eliot Coleman, Mel Bartholomew, Mark Diacomo, Bob Flowerdew, Jennifer Bartley, and Babara Damrosch. Good luck.

One word.........coldframe.

Typically 4 weeks works pretty well for lettuce from seed to transplant and another 4 weeks from transplant to harvest. I wouldn't condemn a coldframe but if you want to have successive plantings you will need a cooler temperature to get lettuce seeds to germinate. A 60F basement works til seeds are out of the ground.

Tomatoes give you more time to adjust to outside conditions. If you have good light in a 50F plus area and can pot-up every few weeks then 10-12 weeks will not be out of the realm of doing. Some people like to set out larger plants from half gallon pots. I've sold hundreds of plants to people who only wanted to pot-up to a 5 gallon container and place it on a deck or balcony for their use. They will usually be pleased with their harvest.

A coldframe used to be the norm for transplant production but now just about every state and country is using plasticulture: low tunnels, high tunnels or greenhouses. They are affordable and give a high value crop like tomatoes a real quick payback. I'll plant tomato transplants in my tunnels almost 2 full months before the last expected frost date in our area. I usually will provide heat (wood) to keep plants warm enough to grow well.

Since you are in a state known for hot summers you might want to look into lettuce varieties that handle heat better. I always either planted transplants on black plastic early and direct seeded a little later but a larger grower in PA has continuous lettuce throughout the summer and they first plant on black plastic, then switch to white plastic.

I live in Mississippi. I grow lettuce outside all winter under row covers. This year it's in pots without any covers and is doing great (mild winter here). Once hot weather moves in, that will be the end of lettuce until fall again. It doesn't like our summer heat at all.

There is no need to start lettuce seeds in pots, though obviously you can if you like. I get my soil ready where I want them to grow and then plant a tiny pinch of seed every 6 to 12 inches (depending on variety). When they come up and get going, I just pinch off the excess plants. To my way of thinking, this is far easier than planting in pots, and besides, light space is too precious. I save that for plants that must be started inside.

I generally start my tomato plants six weeks ahead of the last frost date. I start them in deep narrow newspaper pots I make. That way their roots can go down without being stunted and I don't have to pot them up before they go into the ground. If your night temperatures start to be above freezing temperatures most of the time, you can take your plants outside (gradually). The more outside sun, wind, and rain they get, the better your plants will be. Just be very sure to keep a sharp eye on the weather and bring them in on nights that are forecast to be below 32 degrees. It IS important to start them early here because once our temps start hitting above the low nineties the plants stop setting fruit. Early is a good thing.

Just to clarify. When I say "take your tomatoes outside", I do not mean to put them in the ground. I just take the potted plants outside. The rule of thumb I live by is when the night time temperature lows are above 55 degrees consistently, THEN I put the plants into the ground.

I find that with lettuce I don't want them all ready at once, so I don't mind too much if some get stunted or crowded in their first pots. The different sizes and vigours in the babies equals a spread of time to harvest. If some are a bit slow to get away once transplanted that's all to the good. (I start some indoors in a cold porch to get early transplants. When I set out the transplants I also sow some in the open ground to provide a succession.)

Thank you Flora. My baby lettuce plants are doing exactly as you described. They are crowded, and some are growing much faster than others. I do believe this weekend I'll be moving the ones that have sprouted to bigger pots to keep there until transplant time which should be around the end of February. Thanks again for your advice.

And Donna that's why I use a coldframe. I have an automatic opener so if it gets hot it opens and lets it cool down and on cold nights I put bottles of hot water in the frame and throw a blanket over it. The tomatoes stay out there until time to transplant unless we're in for an ice storm. I use tunnels after transplant but the weather is too variable here to use them unless it far enough into the season to be more consistent.

As for when to take them out.....well if the weather is good I take them out at about three inches. I've done it earlier if the weather is really nice but since I don't like to move them back and forth I usually wait.

One thing to note is that once you take them out they grow fast. Even with shorter days, the sunlight is much stronger than your lights. I've had them grow so much that I've taken to starting them later and still having big plants.

Precisely. The shuffling in and out is a pain in the neck. SOME day I will get a greenhouse....maybe. A cold frame would have to be really big for all the plants I start, but it's an excellent suggestion. I guess the point is, you have to be aware of what you are doing and then make a plan for how you will accomplish it. Without a doubt it is a very good thing to get baby plants outside into sunshine as soon as possible. They will be stronger, sturdier, better in every way.

donnabaskets, you will never regret the day you get your first hoophouse. It's only around about the fifth one that you start questioning your own sanity.

LOL! I think that happened on the fifth set of lights!