what are you using it to cook? Cooking on the BBQ is not intrinsically unhealthy and it's often a good low fat cooking method?
But a few ideas for things to do:
Make lamb skewers using neck fillet. Marinate the meat in lemon and olive oil, rosemary, thyme after you've cut it into chunks.
Thread onto the skewer with a combination of peppers and tomatoes between (aubergine also work well). Brush with the olive oil mix, sprinkle with salt and pepper and cook on bbq.
You can serve as skewers. OR.... remove the cooked meat and vegetables from the skewers and mix with prepared couscous. You can just pour a little olive oil over the lot or you can make up a dressing - lemon, oil and yoghurt. Or go for something with tahini - lemon, yoghurt and tahini. Sprinkle with your preferred herb - chopped mint is obviously good. Also parsley. SIL would probably toss some pomegranate seeds on top.
these are an absolute winner and when DH was a veggie I made them all the time. Am planning to make them for our next bbq (they also freeze well, pre cooked - I used to make up a big batch and freeze individual portions).
A nice veggie side we do sometimes is to wrap asparagus in parma ham and grin on BBQ. A friend always cooks her corn then sticks it on the BBQ for a few minutes at the end. I haven't tried this personally but I think aubergines cooked on the bbq would work well (cut lengthways in half) then served with some kind of sauce or paste - miso would probably be my choice.
Chicken pieces work brilliantly on the bbq but are probably best precooked. Marinate them with your preferred marinate and cook in the oven, covered, for about 20 minutes. Then remove to the bbq and cook to crisp up the skin, brushing them with marinade regularly.
I personally never do fish on bbq but I lots of people who do. Mackerel or trout is a particular favourite. I'm sure you could get instructions online.
DSIS cooks a butterfly leg of lamb on her gas bbq and it comes out beautifully. Again, search online.
Otherwise, the secret with a bbq is to make sure you have lots of lovely and delicious salads so that you're not relying on burgers with the only veg being a thin slice of tomato in the bun.