Short answer, no, this will not work. Lobster and fish are not good together. As for the fish themselves, I would not have platies and gouramis together especially in a 20 gallon. Either one or the other.
The Dwarf Gourami is still a fish with disease issues depending where it comes from--and I don't mean the store, but the breeder. Best to avoid this fish unless you obtain it directly from the breeder and they are reliable.
Water parameters are not mentioned, and this could impact these fish. The GH , KH and pH of your source water needs to be known.
Byron.