I have seen various arguments about the validity of vegetarianism as a core tenet of Hindu moral thought. I would like to set that aside for this question and focus just on the belief systems within Hinduism, Jainism, etc. that either forbid or discourage meat eating. This would include Ayurvedic ideas about meat being tamasic.
I assume the logic may be subtly different in the two cases of plant based or lab grown meat. When I say plant based meat I refer to things like "Impossible Burger" or "Beyond Meat" where they extract substances from plants (such as peas or soy beans) and put them through various industrial processes to approximate the taste and texture of real meat. As I understand it, the only living things killed in this process (aside from side-effects of industrial processes, like pest control in warehouses) are plants so they're technically considered vegan.
When I say lab grown meat these are things that don't exist yet. But in theory it would be more like a cellular growth culture that uses real animal cells to create real animal tissue, but there is no nervous system or brain involved. Functionally it would work almost like growing meat hydroponically. In theory depending on how the technology works this would could be about as violent as picking fruit from a tree, harvesting a tuber (like garlic) in a way that kills the plant, or killing/harvesting a large colony of fungi.
Another corollary to this question would be beliefs about lab-grown beef specifically among non-vegetarians.