I’ve been tinkering around with Hope brakes for 10 years now. I think I have cracked how to look after them and learned the “dos and donts” now (I hope).
Maybe you need a seal kit. These are available through chain reaction cycles.
Make sure the piston sleeves in the caliper are free of any pitting. This is caused by grit and mud – corrosion. If there is pitting you will get leaks and air getting in will cause the lever to go spongy. In this case, you will need a new caliper body.
A full service will at least enable you to give the whole set up a good clean and see what it’s condition is.
The seal kits used to do both caliper and lever. I’d do both if I were you.