I don't believe that low carb and sugar free are mutually exclusive - sugar is just another form of carbohydrate so for me they're really more or less one and the same.
The first thing I did on diagnosis was to cut out all obviously sugary food, as that was what I was told to avoid. Other high carb starchy foods came a bit later when I realised that they were all part & parcel of the same thing. When I started a "proper" low carb high(er) fat diet I also started checking all possible
added sugar/carbs sources by taking particular note of what nutritional labelling says. I definitely agree with
@azure (and others) that eating as much fresh unprocessed (and low carb

) food as possible is the best way to go. For me low carb fruit and vegetables are an essential part of my diet -
not for their carbs - but for the vitamins and minerals they contain, and we need.
I've never liked or used artificial sweeteners so initially wasn't prepared to consider them in my new diet anyway, but I discovered that - particularly in baking - sometimes a sugar substitute may be needed, so after some research I'll now use erythritol and/or stevia, both of which are considered "natural" and have no impact on glucose levels and very few or no side effects. These together with a very few processed foods that have a
little added sugar or other carbs (when there's no available/suitable alternatives!) are a reluctant compromise but one I feel I need to make if I'm to continue low carbing comfortably long term. But this is a decision every diabetic needs to make for themselves and their particular situation, and I don''t believe that one option suits all. The very few times I've ever actually craved
real sugar have been when my body has - sometimes mistakenly

- told me my glucose levels are going too low.
And at the moment unless I'm very stressed or ill, I can keep my glucose levels down below mid 6s for the most part, and in the low pre-diabetics levels with my HbA1c results - which means that as far as I can see I'm managing more or less to get things right.
Robbity