I'm really skeptical about Lenovo because of the proprietary software issues they've had, even read things about bioses with sketchy stuff in them which couldn't be flashed and such.
Lenovo has (at least) two lines of laptop products, one consumer and one enterprise.
The consumer line is shit. It's branded just "Lenovo", but Lenovo themselves call it "IdeaPad".
The enterprise line is good. It's branded "ThinkPad", or "Lenovo ThinkPad", and every unit in this line is bound to have the label "ThinkPad" on its body prominently displayed. The two series of laptops your parent referred to are both ThinkPad series.
And the sketchy stuff you refer to all happened in the IdeaPad line, no ThinkPads were affected. Lenovo has historically run the ThinkPad division separately with some autonomy granted.
Op asked about a laptop with linux compatibility. I'm assuming that's going to be installed from scratch without any marketing/upselling software from Lenovo.
P50 is quite thick, 24-29mm. I'm using T440p and the height is a bit annoying when typing.
In addition to the missing quad-core slim models, another annoyance with Lenovo is that at least the online configurators are still offering just 512GB SSD. It is of course possible to throw in what you want, but if it is not official Lenovo stuff, then it is not covered by the onsite warranty.