2x10 to 1x10... no new cassette and chain normally. You're only usually changing the chainring set up at front and binning the front mech.
But yeah if you're getting the General Lee then depends how worn the cassette is but also the chain. Worn chain will mesh fine with worn cassette but not with a new General Lee so you'd end up with skipping on half the cassette. New cassette will balance it out but then worn chain on new cassette will skip too, so new chain.
Maybe keep the current cassette and try that first then decide if you really want the General Lee as it's a fair expense. You doing particularly steep hills?
Oh, and the General Lee only works with SRAM cassettes I think, and may have to be the higher spec ones. Unless they support Shimano now too. It's all to do with the spider arrangement and how many seperable pieces they come in.
p.s. I'd recommend getting a thick/thin chainring. Something like a Works Component, Wolf Tooth, Raceface and I forget who else are doing them, aside from SRAM on the XX1 of course, though you could do that if you're willing to fork out for an XX1 crank - which will work with 10 speed. But the other options are much cheaper, and work perfectly. You won't have a dropped chain with those, especially paired with a clutch mech.