Although at first it seems to be illogical, friction levers need some grease to even out the friction across the whole range of lever movement, otherwise you have places where the lever slips. It also allows you to tighten the pressure screws sufficiently with your fingers rather than having to resort to tools.
Clean off all the manky grease and dirt then put a thin smear of grease on every mating surface, you don't need much.
I didn't believe the advice at first but after a season of gears jumping at awkward moments I was willing to try anything - after that I rarely suffered from slipped gears again.