Audio technica AT6006R tonearm lifter

I agree with needing increased friction, but check the antiskate setting.  To move the arm over the lifting section of the AT6006R there may be excessive lateral force being applied or insufficient VTF.

I agree, it should not pull out via anti-skate, and as you say, you used it for years successfully.

Is the top of the lifting arm’s rubber surface worn/polished too smooth? Fine sandpaper to restore some grip? Even cut some small indentations.

Is the TT perfectly level? check platter separately/check arm post separately. i.e. arm perfectly perpendicular to the platter.

Zero anti-skate: does the arm float or pull in/out when balanced parallel to LP?

You could shim the lifter slightly so that there is a slight rise in the top bar to lift and resist inward motion.

Falls off to the outside or the side away from the spindle aka in the direction of the AS force? If so, then maybe you can glue a stopper to that side of the lifter arm. Or just dump the lifter. It does not damage the stylus to ride for a few extra seconds in the runout grooves.

Yeah I would put a little blop of silicone on the outer edge of that lifter to act as a stop. 

lewm, woof

good solutions, however, like mine and others are 'tricks' to solve a problem that should not exist.

I think something else is OFF, and should be tracked down as whatever is OFF might/must be affecting ____ while playing.

Had a similar issue myself. I used the information for setting anti skate provided in the link below. Corrected the issue for me. 
 

https://www.sound-smith.com/faq/how-do-i-adjust-anti-skating-my-cartridge#:~:text=For%20a%20given%20VTF%20(any,VTF%20required%2C%20for%20ANY%20cartridge.

Thanks all.

I had another go today with a few tools. Turns out it was running with too little weight (1.65g, alpheta 2) and too much antiskate. I ended up covering the top of the tonearm lifter with a thin layer of blutak. Works great now.