Reading the bit about the stairlift not working if the power is off, would suggest to me that the battery is kanckered (technical term) or the charging circuit is defunct..
What may be happening is that the charger is powering the Lift and is not designed to do so, so in effect is being overloaded which will likely cause a lot of interference.
The fact it happens at different times of the day would also reinforce the above, I`ll bet it only happens when the lift is in actual use, if the charger is actually at fault it would be constant - the charger is connected by a spur so will be always on.
It could be a combination of all the above, of course I may be wide of the mark on all above.
If I was the owner I`d be pretty peed off if I got stuck halfway up the stairs during a power cut.