An extended use of l-lysine shouldnt be harmful, seeing as how it is a supplement designed to help a cat’s immune system. My Luna is always so sick I am trying to get her back on it. I think she got 1mL twice a day (it was a syrup) but she loved it so much.
As for the pill, try to get something very smelly and flavorful. Like, a little bit of tuna or something. If that doesn’t work you will have to force the pill. You will have to cup your hand across her head putting your index finger and your thumb at either hinge of her jaw and lift it upwards so she is looking up. Then with the other hand, open her mouth, toss the pill down her throat, close her mouth and keep it shut. Then rub her throat until she swallows and licks her lips. When a cat is grabbed on either side of their head, they are almost powerless to move it. Just make sure she doesn’t hide the pill under her tongue.
I’d say, next time go for the syrup. It is usually cod flavored and cats adapt to it very well. Plus it is easier to give it to them. I would say if you are having trouble, mash it up really fine, mix it up in a lot of smelly stinky fish flavored food pate, and if she won’t take it just start spoon feeding her the mush. Keep putting it in her mouth and on her tongue and hopefully it is just tasty enough to eat up. If that doesn’t work you will have to resort to the above method.
L-lysine is found in a lot of cat foods so I wouldn’t worry too much about extended use. I gave Luna l-lysine for 3 months straight and no problems. Good luck!