sowing lettuce indoors over winter

because my garden is brand new I wont be sowing any veg until the spring but I wanted to have lettuce variety over the winter. sowed couple of varieties of spinach and lettuce 2 weeks ago in flat boxes of seed compost and have them in a sunroom at around 19/20 degrees. seeds have germinated but seedlings dont seem to be growing much and very spindly and not upright (look like they are falling over!) but soil looks moist so cant be under watered. am I too impatient or how long should I expect seedlings to start thriving? do I have to thin them if Im growing them in the boxes for cut and come again? or can I just leave them and wait…?