Anyone used car upholstery cleaner on jacket lining?

I need to clean the quilted lining of a vintage leather jacket, there are some old stains (that I doubt will completely disappear) and some smell mainly in the upper back and pit areas. I don't want to bring it to a laundry fearing damages to the leather.
I already tried some water/vodka but it didn't change much. I would eventually try also baking soda or white vinegar, but I was wondering if anyone ever tried one of those spray/foam cleaners for car upholstery/tissues, or even dry shampoo on a jacket lining.
Or maybe these are too aggressive and could damage the lining?

 

I don't know the material, it's a Fidelity crosszip jacket probably from (late?) 60s, probably synthetic but I am not sure, also don't know about the filling material, here is a pic (with the stain)