You have 2 categories of variables you're looking to test in terms of their optimal performance, the LP and the ad. You will be testing 9 potential configurations. LP1 + ad1, ad2, and ad3, LP2+ad1, ad2, and ad3, and lp3 +ad1, ad2, and ad3. You must account for every possibility. If lp 1 + ad1 does better than lp2 + ad2 then you don't know whether it's the LP that provided the increased CVR or the AD or the combo of both. So you have 9 subids to make basically. If you have your own adserver or google website optimizer or whatever just 33/33/33 rotate the ads with indiv subids and 33/33/33 rotate the lps.
The reason you want 9 subids to begin with is that if you just choose the ad that performs the best on LP1, it
might not perform better than the alternative LP1 ads on LP2, but you'd never know this because you only tested the ad that did best from LP1.
I don't mean to overcomplicate this. Just test the 9 variations so you factor everything into account. That's how multivariate testing is done.
This might be obvious to you, so forgive me if it is, but if you want to compare the LP's alone irrelevant of the ad then just compare lp1+ad1 to lp2+ad1 to lp3+ad1. Keep one variable the same and change the other.
Multivariate testing is this: You have a single ad with 5 typefaces, t1, t2, t3, t4, and t5. You also have 5 different images of a person, p1, p2, p3, p4, and p5. You also have 3 different backround colors, c1, c2, and c3. In order to account for every single variable you must have 5x5x3 tracking IDs. 75 total ids. The big boys track hundreds if not thousands of these potential variables in high level optimization.
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