If you already have the Lime, it will be the best choice for VLF in the SDR world. Yes, it has a downturn in sensitivity. Heck, it almost covers 4Ghz.You will definitely need an antenna that is somewhat worthy of the signal that you are trying to receive. A 1/4 wavelength will be a couple thousand feet long, as a guess.
When working VLF, you need specialized equipment. Add about $100 outboard tot he lime (PC not included) & you will have a fine VLF transciever.