Reading this, I now realised I did something similar but with a 2 hour cushion instead of 1, in a much larger airport (ARN) than LUX, and with checked luggage.

I was travelling SK ARN-CPH-PVG, using DY LGW-ARN (first flight of the day, on a Thursday) as my positional flight which landed on time and luggage came out fairly quickly.
I didn't think much of it at the time, and thankfully everything went pretty smoothly. But thinking back, If the DY flight went tech or had weather delay, I would be screwed big time.

So take the advice from the others and book an earlier flight.
BA does LHR-LUX - BA0418 lands at 17.30 and BA0416 at 11.10 (£57 HBO). If you have never been there you could spend half day tour around "world's only remaining grand duchy".
You could also take Luxair, LCY-LUX on LG4594 arrives at 13.25, though cost £100.