Hi Jimgif
No matter what curry you have, whether it be a Balti (and there are many different types), or Dhansak, there should never be a dominant taste of lime .. or any other souring agent.
Lime is used to add a subtle sour taste, as is lemon and lemon juice, tamarind, ambchur (mango powder) and to some extent, pineapple.
I guess by far the most common souring agent used in BIR's is lemon juice, but this again should not dominate the taste of a curry.
As far as the sweetener goes, the most popular ingredients are jaggery, palm sugar, dark brown sugar, mango chutney even honey. White sugar should not really be used as imparts sweetness, but no taste.
If your local is supplying curries that constantly have a dominant taste of lime, I would mention it to them. If they persist on overpowering the curry with it, then go somewhere else. It ain't right.
Regards
SnS