Wow - where to start?

First big question. Have you grown any herbs from seed before? If not it might be a good idea to crack that first before moving on to the pallet garden idea. Not all the herbs you mention are easy from seed. Even the ones which are will not make transplantable plants inside several weeks. Some e.g. lavender and thyme will be a couple of months before you have a plant big enough to transplant.

I have not, but i also was not really planned on transplanting them. Do they NEED to be transplanted?

The transplanting makes it easier because they have already grown 4-6". At that point, all you do is cut a spot in your fabric (that is holding back the soil) and put it in.

Otherwise, your seed should grow through that same spot if you go with seed. But with the vertical challenges of keeping things watered, the seeds or seedlings may struggle.

I know some people have seeded directly into an earthbox (which is also customarily covered by some fabric or material) but that is a more typical horizontal planter, so the water needs are not any more of a challenge than for other horizontal planters (and probably even less so for earthboxes)

The herbs you mention will need different conditions to germinate so it's much easier to sow them in pots and then transplant. Lemongrass, for example is a tropical plant which needs high humidity and 70 - 75 f to germinate whilst lettuce will not germinate above 80 and can germinate at much lower temperatures. (Lemon grass is actually usually grown from cuttings not seed.)

Another advantage of using transplants is that you will not have to look at an empty container/pallet for weeks on end while they germinate but will start with a full display.

Ditto the earlier posts-you have a lot of variety there, and some are definitely more difficult than others. You'll have to do more research on the individual herb needs. I would start with one of your pallets on the lettuce, plus maybe the parsley and cilantro which are easy seeders and do some learning on the others. Garlic chives are also easy seed, though they take more than a year to come to maturity- you can use them sparingly when small, but they're pretty puny. Get used to the care of the pallet garden before trying some more difficult ones.