I've always thought that the main visible difference between the Lee and the Grant was the turret.
In the book British and American Tanks of World War II (Chamberlain and Ellis) as one would expect a photo of an M3 (with the British turret) is called a Grant I and a M3 (with an American turret) in British service a Lee I. However, a M3A5 (with American turret) in British service is called a Grant II.

Note that while the book gives the number of each variant produced it does not have a breakdown on which turret was installed. It would be interesting to know how many of each variant were produced with the British turret and how many with the American turret.
Correction: It does say that Pressed Steel Company and Pulman each received an order for 500 M3's with the British turret, so one would conclude that other variants in British service had the American turret. But the M3A5 and M3A3 in my posted links ("M3 Grant-confused" thread) have British turrets.