@SportyJordy, are you on the latest firmware for the LZW31-SN? If not, some changes made after the original shipping firmware may have helped with this. A few people had problems with smart bulbs flickering or even turning off with early LZW31-SNs, which recent updates may have helped with. A recent one also added a "smart bulb mode" parameter to ensure that the dimmer is always at 100% (Z-Wave level 99) if the switch is on, which is a problem some people ran into before, though I'm not sure it really adds anything you couldn't have already done yourself by being careful. I believe earlier revisions are supposed to have addressed a possible root cause of this other problem.
You can find the updates on Inovelli's website or forum, and you should be able to use the community Z-Wave Firmware Updater tool here, the newer "binary" version, to update both targets 0 and 1 as instructed. Alternatively, an external Z-Wave stick using Z-Wave PC Controller may be faster if you have one.
Also, do you have a neutral wire connected to the dimmer? If not, there is a minimum wattage you'll need for the load, or otherwise you can add a "bypass" to it to lower that (but it's still something like 6 W with one, I think). You've probably read this in their docs, but I thought I'd mention it if not. The wattage you see, as you may know, is just a power report from the switch--the dimmer isn't reducing the power sent to the load; the load is just using less power through the dimmer. That being said, even with a neutral connected, I still had problems like yours with one of my dimmers. I don't think I've noticed anything since using recent firmware, but I'm no longer able to test that in one of my rooms since I just rethought my setup to avoid that problem in the first place...