If he's used to a lamb based kibble it seems pretty unlikely. Hopefully he isn't developing an allergy to lamb. It can happen over time and it really sucks because you have to change foods.
My dog throws new treats up fairly often, but it's because he gets so excited that he forgets to chew. How much time passes between treat and vomit? Do the treats come up whole?
Keep an eye out for excessive scratching. That's a pretty frequent symptom for newly developed allergies.
I really hope it's nothing. Seems like you've already got enough going on without a sick doggy too