So, a bit of stuff that I've been looking around:
To record the stuff with a physical knob, I needed to link my phsycal knob to the digital one of LMMS manually (the one you drag to the automation track), this is a thing I do all the time, since for some issues some VST don't get my knobs on them instantly or do it in a way I don't like it.
As long as I've experimented with it, it worked, but If you're using a knob to record the thing and then you play it again, the knob has preference over the automation track (it seems) and the actual state of the knob will override the state of the automation track.
To solve this I just unbind the knob from the...eeh... digital knob, so it can go around freely with the automation track.
Maybe you're recording with the knob assigned inside the VST and so LMMS don't get it (dunno, I haven't tried to record this way ever, always put the knob manually), or maybe you need to unbind the midi for it to work, but as far as I've read, the thing is that it doesn't record the stuff, not that it doesn't reproduce it, so give it a try to assing the knob in LMMS rather than inside the VST.
Hope this helps.