Is there any rule of thumb for comparing lights rated in lux and lumens? Currently, I'm using a front light rated at 35 lux on my bike. This is just about bright enough for my riding, but I'd like something a bit brighter. However, most of the lights which might be brighter are rated in lumens, rather than lux.

I'm a physicist by training, so I know the difference between 1 lux and 1 lumen and that you can't compare them directly - but that doesn't help me as I do need to compare them somehow. Is there any rule of thumb or something that I can use to work out which lights are actually brighter than my current light, or does the beam pattern of lights vary too much for this to be a sensible comparision in any way at all?
I don't think you're going to be able to do any reasonable conversion, since lux without a distance is meaningless. It's likely that the manufacturer has picked lux specifically to make it sound impressive, or possibly even to make it hard to compare.

Here's a nice description of the (optional) standard: http://www.led-resource.com/ansi-fl1-standard/. One of the possible measures in that standard is the distance at which the light is 0.25 lux. Another is the candela (peak beam intensity). And, of course, there's always lumens (total output). Lumens seem to be the favorite.

Instead of trying to compare the brightness of your current light, I recommend visiting this great light comparison site (which originally started from some posts on our blog): https://www.bikelightdatabase.com/

In particular, the beamshot photos on that site are super-useful. There can be big differences between lights that use the same measurement (usually lumens) and being able to look at what that looks like on a stretch of road is amazingly helpful.