Hi Mo
When you say LCHF, how low do you go? e.g. 100g a day or 30g a day?
I am a soup addict, I have soup nearly every day (even in the hot Australian summer), it is my comfort food and a great way of including more veggies in my diet.
My favourite soup is made with red peppers, tomatoes and carrots, stock, dollop of cream, chilli, smoked paprika. I have a vitamix which blends it down to the consistency of tinned soup.
Another one I like is cauliflower, broccoli & watercress ... boil it up in some stock, add some cream and blend til smooth.
If you eat carrots you could make a Thai Carrot Soup with coconut milk.
Hope that gives you some ideas. I also sometimes make a French Onion Soup topped with grated cheese (no croutons though!)