I think you mean the lever itself sags? If so the pivot pin hole in the lever is probably wore out.If the pin looks good(no wear groove in it) and the pin fits snug in the handlebar mount and the slot the lever pivots in is tight try a new lever.Lots of times both the lever and the slot will wear letting the handle sag.
On an old bike like that? Likely you need to rebuild the brakes. May need new seals in the master cylinder. New brake lines, fresh brake fluid, possibly a caliper rebuild, etc. You could try fresh brake fluid and bleeding the brakes to get all the air out and see if that fixes it on the cheap - for a while.
The first step is to figure out why it is saggy. I would change the fluid and the brake pads (if less than half). Use a good brake line vacuum and flush the old fluid out. Open the line just enough to get it started and keep the master cylinder full. I had one of these bikes and the fluid was never changed, and the fluid had turned to a gel. Once I cleaned everything out.it was like new. Good luck with it
They didn't bleed the brake lines. It's fine though.
