i would direct seed them. gonna be hard transplanting 576 lettuce plants a few inches apart from each other. easier to direct seed and thin as needed.

If you want to start them indoors you can make a cheap grow light set up with shop light fixtures and fluorescent lights hung with light chain from a shelf or the ceiling.

You will also need soils starting mix (no ferts in it), seedling flats to out the soils mix into. This will cost you no more than $75 for everything and likely a lot less if you have some of the equipment

I've sowed lettuce seed into trays of vermiculite, then pulled the sprouts out to transplant into cell trays. The vermiculite makes it easy to pull them out without damaging. If your seedling is leggy, each time you transplant it, you can stuff it a little farther down into the cell or pot.

Look into soil blocks - you can start the seeds in the tiny blocks on a seed heating mat and move them up to larger blocks as needed. Or plant them out.

The seedlings will survive weather that is too cold to sprout seeds in.

Also consider the colder-weather greens like spinach and chard.

NOTE: I have not done this yet, but will be doing it next spring.

I have used soil blocks for over 20 years and love them but you still have to buy or make a soils mix from which to make them.