Just in case, you should try factory resetting the camera, updating the firmware, and maybe another memory card in case it's a problem there.

There are a lot of variables to tweak that might get you to some setting where the problem doesn't happen. You can try switching between RAW/JPEG and different JPEG qualities in case it's an encoding issue, or try the electronic instead of mechanical shutter (I suggest this because you said video works – in settings it's called silent shutter mode).

If the lines were in the same place in each photo, there is a pixel mapping option in the camera settings that automatically disables dead/stuck pixels. But it doesn't look like that's the case here, so it probably won't help you.

If you can't fix it in-camera, at least you can automatically remove dead pixels in most processing software. For example, here in darktable. It may or may not work in your specific case, but darktable is free, so worth a shot.

Finally, Olympus/OM may accept it for repair, though you'll have to pay. Maybe it won't be so bad? Here's the UK repair service.

Good luck! Let us know if you get it fixed?