The lining isn't very thick, as in it wouldn't be mistaken for a down jacket. I'm not sure if this is useful but here's a photo looking at the thickness of the lining. The fit issue was more in the shoulders, the coat is fairly fitted across the chest and in the shoulders with high armholes, which looks great but makes it a little less forgiving fit-wise. I have a single breasted coat as well and it fits more like suit jacket than an overcoat, which I really like.
Hope that helps, let me know if you have other questions!
Hope that helps, let me know if you have other questions!