so do people just keep little lobsters like this on their own? what do they eat??
they get kept on their own, again if you go for a legal cray, in the uk, you will need a tank of minimum 20ukg, but 30 and above is better. they need hides, caves, pipes and that sort of thing. they are into tank rescaping, big time. escape is also a well known hobby of the cray. they eat anything, but mine loves: fresh peas, not boiled, just skinned, cucumber, plec ground pellets, fresh chicken, roast,and fish flake. i would advise you avoid bloodworm, as they are very high in fat. i have also heard it said, a fair amount of bacteria too!
lol you say little

a redclaw will grow to 5 to 8 inches, and that's just nose to tail, add 2 or 3 inches for the claws. and a further 8 inches for its antenna

not really that small. they can live for 3-8 years, but 4 to 6 seems average.
just a personal comment: plecs may be slow, but they are also armoured, i have 3 in my tank, of all my fish they are the ones that i worry about least. having said that, if a cray wants a fish it will get it, but then a cray with that disposition should not be in a tank with fish.