not sure that tallow and lard are necessary, but here's an interesting article that does suggest frying with saturated fats such as coconut oil or ghee, or alternatively, unrefined mustard seed or canola oil. It also has a table with data for several kinds of fats. The disadvantage to animal-derived fats, according to this, is the long-chain saturated fatty acids.
Interesting table - very easy to see which fats are the worst. It's a pity they don't include animal fat in there but I guess it's all from an Indian context. Coconut seems like a good option but it can still go rancid if you don't refrigerate it.
Some the early citations [2 &3] are not the best quality as they are based on questionaries. In the Minnesota Coronary Experiment which involved 9400 institutional participants eating controlled meals they found that cutting saturated fat can reduce blood cholesterol but that doesn't actually make one live longer. https://www.scientificamerican.com/article/records-found-in-...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4990724/