Not really, but only because I haven't had the opportunity. He's not a big eater, I don't really make anything specifically for him, he just shares our meals. So if we use oil in our food, I don't not give it to him, kwim. I'm sure olive oil is perfectly fine. Or coconut oil would work well too. Honestly, I don't avoid much with him. I don't do nuts and honey obviously, and have been avoiding dairy of course, won't give him anything I don't feel is healthy enough, won't give him anything with salt or sugar, and have sorta been avoiding tomatoes, citrus, and berries. Other than that I've just been passing him all sorts of stuff.
You can do lumps now, but I'd go straight to more finger foods as he will learn how to deal with the lumps of food in his mouth faster than off a spoon.