In case of my stubborn right Shift that would stick if pressed at certain angles, a q-tip and some silicone spray fixed the problem (I think I used that on both the stabilizer and the stem in the end). So yes, a bit of lubrication seems like a good bet. Silicone or teflon (PTFE) grease/spray, preferably pure, would be some good options. Don't overdo it though, silicone grease in particular likes to creep everywhere.
I have a feeling that early Ms with their proper stabilizers would be less susceptible to such issues, but it's hard to prove.