I'm afraid that I can't help too much with the acronyms. All I know is that UC stands for Upper Canada which is now Ontario. I can only speculate that DR and IR refer to whether or not Lavender was present for duty or detached somewhere else. In 1815, the Detroit command consisted of Detroit, Malden, Sandwich, and Fort Gratiot.
To muddy the waters even more, Congress authorized creation of the 24th Regiment in January 1812, but recruiting didn't begin until June. Soldiers could then enlist for either 5 years or 18 months. The 2d Rifle Regiment was authorized in February 1814. One of the 2RR company commanders was Benjamin Johnson who had previously served in the 17th Regiment of United States Infantry. Lavender's enlistment into the 2RR was probably May or September 1814 and the 1813 date is a "typo". By that time, the enlistment options were either for 5 years "or the war".
You're right about the lack of information on the two regiments. I've been squirreling around with the 2d RR for a couple of years now and haven't had much luck.