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The information I have read on this subject states that vitamin C appears to have an impact. The amount could be a subject for your project. Give each of say 5 different lima bean plants different doses of vitamin C to see which dose provides maximum benefit. Too heavy a dose will lead to death of the plant I am sure. For years I had heard of the benefits of vitamin B-1, however in the last 5 years I have read some articles that say it has no real noticable benefit to the plants. I personally have seen the strong effects that a product called Super Thrive has on plant growth. Not sure what all vitamins are in it as that seems to be a closely held secret.

It sounds like you may have a high nitrogen problem. High nitrogen will produce big plants, but few seeds/pods. Have your soil tested and cut back on nitrogen while increasing phosphorus. The phosphorus will help bring the plants back into balance so they can fruit.

It sounds like it may be a pollination problem. If pollinators can't get to the blossoms, there will be no fruit. Common causes of pollinators not being able to get to flowers include pesticides, heavy rain or very hot weather. This article will help explain more: https://www.gardeningknowhow.com/garden-how-to/beneficial/insect-pollination-process.htm

And this one will help with getting pollinators to your yard: https://www.gardeningknowhow.com/garden-how-to/beneficial/creating-a-pollinator-garden.htm

If you have good soil, they don't need much fertilizer. A bit of balanced (e.g. 10-10-10) fertilizer will be fine. They do not need lime. Lime is sometimes used if the soil's pH is off, but the average vegetable garden does not have this problem.

Fertilize with compost or an all-purpose fertilizer as a side dressing. However, avoid nitrogen rich fertilizers because lima beans do not require extra nitrogen.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/vegetables/beans/how-to-grow-lima-beans.htm

It makes no difference which way you drop the seeds in the ground. They will grow. Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/edible/vegetables/beans/how-to-grow-lima-beans.htm
https://www.gardeningknowhow.com/edible/vegetables/beans/tips-for-growing-beans.htm