You should pick lemon cukes when they are the size of a small lemon. They will still be green in color but tender and yummy. My favorite kind.
I think what your soil is missing is manure. I use steer manure because is cost about a $1 a bag and its mild. Mix 1/3 to 1/2 steer manure and the rest your soil. Get it completely wet before planting your cucumbers or you will burn their roots. Toss some time release fertizler in there too.
Daisy