mrw--
I'll let someone else address transplanting your
seedlings. I've never started beans indoors. Lima beans have one of the highest optimum temperatures for
seed germination. Ideally, the *soil* should be about 85 degrees when you plant the
seeds (down to 60 degrees is o.k., but germination time will be longer). I suspect that you may have planted your
seeds too early last year.
You don't say where in NY you are, but if you check the hardiness & frost date maps on this site (up at the top), you'll see that for most of the state, the median last frost is in May. If you don't have a soil thermometer, you can guesstimate when the soil will be warm enough because lima
seeds should be planted about two weeks AFTER the last frost date. And as always, it's better to be a week or two later than early.
Hope this helps!
P.S. Last frost in may area is 5/1-15 (depending on who you ask), and I don't worry if my limas aren't in the ground until 6/1-- plenty of time for them to mature!