Answer: First off, I hope you are growing pole limas rather than bush type limas. Next, the seeds will germinate best with bottom heat and constant humidity, so you might try putting the pot in a plastic bag until the seeds sprout at which point immediately remove the bag and place them in bright light. In the garden limas absolutely need full sun, so they will need as much light as you can give them if they are to be healthy plants. Ordinary fluorescent light placed close to the plant for 12 to 16 hours a day should be plenty. However, for your experiment you will need to alter the light conditions so you will have a bit of a challenge in keeping them growing while causing them to stretch for the light!
A week is perhaps a bit soon to expect germination especially without bottom heat (they may have rotted if too cold and/or too wet); if you are truly worried you could gently dig up one or two and see if there is any activity and then gently replant if there is. Should you need to try again, you might wish to use a sterile seed-starting mix slightly dampened, clean plastic containers covered with plastic wrap (this helps maintain constant humidity), gentle bottom heat, and plant the seeds so that they are just barely covered.
Finally, tiny seedling roots can sometimes be damaged by excess fertilizer, so rather than sticks I would suggest a water soluble fertilizer applied about once a week at about a quarter the usual rate starting after true leaves have developed. Good luck with your project!
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