Early lab meat is going to have weird texture problems because it's missing all the details that come from how a specific muscle connects to ligaments and the circulatory system and whatever. Solving this will be hard and require more fundamental research. Swapping what animal the cells technically come from will be pretty easy. So as soon as lab meat is viable, expect businesses to suit their need to expand by exhausting all the animals they can market. And the list of animals people have heard of is pretty short, so expect human pretty quick.