wait for your blood test, just keep cutting the carbs, including fruit...so whatever insulin you do have, can work on the protein, fats and non starch veg
if you weren't trying to lose and eating enough,,losing weight is a symptom. LADA can take years before you don't produce insulin, or you may be T2..either way you need to get your Blood level down
you can put on weight with protein and fat after your body gets use to it, as you know cutting the carbs is keeping your sugar levels down a bit.