(a) is incorrect. It should say, "Cut the lemon in half. Take one half of the lemon and slice it."
(b) is correct as it is, but I think the corrected version of (a) sounds a little better.
If you are giving directions it might also be a good idea to specify the number of slices you want the lemon half cut into. For example, you might say, " Take one half of the lemon a