I don't know much about the history of Aston Villa but I understand that there were Scotsmen amongst its founders and that one of them in particular was born and bred in Glasgow.
George Kynoch established his works at Witton in 1862. It grew rapidly and soon became one of Birmingham's biggest factories. George was born in Scotland as well, not in Glasgow although he spent the early part of his career there. Very early on in the life of his Birmingham company he adopted the name "Lion" for his works and also seems to have used the image as a company logo. He was a patron of Villa and became its President in about 1886 at around the time that he was also elected M.P. for Aston; a couple of years later he disappeared entirely from the Birmingham scene.
Beyond that, the connection between the lion emblem on the one hand and the Company, Villa and Rangers on the other seems unclear, although perhaps more than coincidental.
Chris