I think your idea is neat, but you have several hurdles:

1) Though your hybrids are all in the legume family(Fabaceae), they are not in the same genus.
Peanut - Arachis hypogaea
Pea - Pisum sativum
Soybean - Glycine max
Lima - Phaseolus lunatus
Generally, it is harder to make hybrids the farther apart they are on the taxinomic tree. Hybrids within a genus are generally easier.

2) The chromosome counts are different for each of these
Haploid number
Soybean 20
Lima Bean 11
Pea 7
Peanut 10

3) The peanut is an allotetraploid -- sometime in the past two plants in the genus Arachis hybridized, and the hybrid was probably sterile -- so a chromosome doubling occured so it has two complete sets of genes from two different species (and its full chromosome count is 40). I believe all the others are regular diploids (2n) or specifically: Soybean(40)*, Lima(22), Pea(14).

But don't give up you may be able to come up with a breakthrough, but you might want to also be breeding something else at the same time that won't be as difficult.

Good luck!

*You may have noticed that the soybean and the peanut have the same number of working chromosomes. I would guess this to be your best bet. I suspect you'd have to have natural or induced chromosome doubling to return fertility.

Good information! What is induced doubling?

Peanuts are not close to soybeans or lima beans. They belong to the Dalbergioid clade, which includes Dalea, Tipuana and many other, mostly New World genera.
Soybeans belong to the Milletioid clade, which also includes Phaseolus, Vigna, Indigofera, Erythrina, etc. Peas Chickpeas, broad beans and lentils belong to the Hologalegina clade, along with Wisteria, licorice, black locust and loco weed, etc.

Here is a link that might be useful: Tree of Life

*Good information! What is induced doubling?*

Induced doubling is by treating a plant or seed with 'something' (usually a chemical like colchicine) you can cause the number of chromosomes to double inside each cell. Since each chromosome can now 'pair' up fertility can be restored. However obtaining these chemicals has (at least in the US) gotten very difficult (also most of these chemicals have some hazard to the handler of the chemical so you need to be very careful).

Check out "Polyploid" in Wikipedia and also do a google search on "Hybridizers: Chromosome Doubling"

Given that I am an organic gardener, that would not jive with what I am trying to do. Good information nevertheless. Thanks!

I thought colchicine was a natural product made from crocus. Am I mistaken?