Hi gardel0. A low carb diet does not necessarily have to be low in fibre. Look into what low carb vegetables you can include (and hopefully enjoy) in your diet. For example, I have been including quite a lot of egg plant (aubergine) and am really enjoying it. I also eat a fair bit of cauliflower too, which is actually pretty nice if you add enough cheese or butter etc to it.
To be honest I was never a huge fan of a lot of the low carb vegies that I'm now eating (and enjoying). However in the past I was always trying to include these vegetables as part of a low fat diet. The difference now is that, since I've dumped a whole load of calories from carbs and increased my consumption of fats to compensate, many of those vegies are now highly palatable to me with added fats like cheese and butter etc.