I believe if you eat a varied and healthy low carb diet, you will be automatically including a good selection of fats and oils from various sources: meat, poultry, oilier fish, eggs, dairy, olives, avocados, nuts, seeds, and their various butters and oils, coconut oils, etc. I like to hedge my bets!
I eat a very low carb/ketogenic diet, and prefer to include low carb fruit and vegetables for their vitamins and minerals, but not everyone believe that this is necessary - it's a matter of (a) personal choice and (b) how well your body can handle carbs. But whatever you decide, it's important to realise that you may probably be eating low carb long term, so you need to make quite sure that your choices are sustainable - and enjoyable.
Robbity