I don't know what form the Lysine comes in but here's what I did for my late kitty who had never been pilled in her entire long life:

1. I crushed up the pill/opened the capsule and mixed the powdered stuff into Whiskas cat milk or even human evaporated milk. I diluted both a little bit with warm water. Don't use too much milk - max 1/4 cup.

2. I got a liquid syringe - mixed the above powder with water or the milk and squirted it into her mouth.

I hope you find a solution.