A. There is no such thing as a "lift kit" and the so called 'rods' are simply cheating while providing nothing truly changing the available height already designed into the system.
B. I had wider wheels than the lr4 stock 20". They were RRS SC 'Stormer' wheels with 285/50-20 and they barely fit. You can hammer/bend back the outer lip of the UCA if it does contact the tire. Nextcsize fit sure would be 275/50 and of course 275/45 but these are all geared toward the wider wheel.
C. If you want to stick with a tire that actually fits your wheel in an ideal proportion, probably that 265/50 or 275/50, you could get it flush with the fender by adding a 25mm spacer from H&R. I wouldn't recommend their 30mm as it could start to push the tire into the tight clearance spots while turning, which even the waste of money 'rod mod' doesn't really remedy. The H&R spacers are very well made. I have both sets.
Verify your wheel width and offset first. Also, do you have a full size matching spare ? If not, you can't use the temp spare if you've changed the diameter of the running tires. You should be getting a 5th wheel and matching tire for the spare.