Hey there Temple Flower-
I copied this out of my notes....
Germinating Lathyrus latifolius Seeds:
Nick perennial sweet pea seeds and soak for 24 hours. Sow outdoors in early spring, 1/4" deep. Or start indoors 6-8 weeks before the last frost date. Hardy to zone 5. Easy to grow. Full sun to part shade. Seeds are poisonous.
It looks to me that you wont be able to put them out in the ground till after the last frost date to be safe.
I have found that sticks or branches put into the pot with them will give them some temperary support. I have been known to carry out pots and trays of seedlings in the am on warm days and bring them back inside for the cold evenings till they harden off or can stand the temps out side and a bed can be prepared.
You may find you will need to transplant them into a larger container to give the roots room to grow till you can plant them in the dirt outside.
I tried to make container plants out of them last year for my mom- but that didn't work too well- even in light containers, the soil was way too warm for them to do well- they were stunted and eventually "baked" in the sun.
I do hope you have better luck than I did with these-
Julie