Given how quiet 2 of those stations are (and Lancaster would be at that time of night) and given how we are talking about a 5 car train, I don't entirely get why staff are even needed. The guard could dispatch and there could be a side gate just as there is at a good many other stations not staffed for the full period of service. For Lancaster you could even close the bridge off with only the northbound side in use.
But this is classic railway.
Staff are needed for safety (& security) it's quite simple.
A guard can not prevent a person who is on the platform from attempting to board/get too close to a train while it's departing a platform. Particularly as most modern rolling stock where the guard doesn't have a window to look out of, the only time they'll know if something is wrong is when the bits come flying past the window.
You could argue that 397s have bodyside CCTV cameras but they only look along the side of the train. By the time the driver has noticed something, bearing in mind they've got other things to be watching as well it'll most likely be too late......
I do feel you're not very familiar with the local situation at any of those stations.....
Lancaster;
Only the down-side platforms 1,2&3 have a side gate, which is regularly used by bike thieves who steal from the cycle racks next to said gate.
A hostel for rehabilitating drug users opened just across the road a few years ago, without going into detail it has resulted in several incidents on the station. Add to that numerous trespass incidents & one-under attempts which have all been delt with by....... The station staff.
If left unmanned with its close proximity to the city centre it probably would become a hot bed of antisocial behaviour, vandalism & some successful one-under's.
Oxenholme;
Quiet? I don't think so....
Pre-covid usage figures collated by the local user group showed Oxenholme generates more London traffic that the other two Cumbrian WCML stations combined. Also pre-covid it had the second highest increase in passenger numbers of any AWC run station.
Post-covid the station is once again busy with those heading into/out of the Lakes & over into the western Dales.
The stations curved platforms and roof pillars create poor visibility & blind spots. In the case of plat1 is also narrow.
Unlike Lancaster all non-stop trains pass through the platforms at up to 90mph.
The station is also a popular shortcut to/from the pub at the top of the hill.
In the last few years there's been two successful one-under's, several attempted one-under's, plus various incidents of public on the track (intoxicated or otherwise). Again all delt with by....... The station staff.
If left unmanned with its out of the way location, close proximity to Oxenholme Village and the housing estates on the western side of Kendal it would again probably end up being a victim of antisocial behaviour and probably more one-under's....
Penrith;
The only exit from the station is from the platform1 side, via a subway with steps.
Penrith's curved platforms (which is even more severe than Oxenholme) makes visibility an issue, even for a 5 coach train.
The new overbridge with it's lifts would need remote monitoring but still not ideal if anyone got stuck in one of them as no doubt it would take considerable time for help to arrive if there were no staff on site.
The station is very close to the town centre and has again been the scene of antisocial behaviour from those who travel up from Carlisle for a night out in Penrith & travel back again over the years.
Also over last few years there's been three (maybe four) successful one-under's, plus various incidents of public on the track (again intoxicated or otherwise). Again all delt with by....... The station staff.
If left unmanned with it's close proximity to the town centre etc, it will end up being vandalised and more incidents of trespass and one-unders.