Just an idea. I have occasionally found that it is worth the little extra time to remove the seat and have a lot more floor space to work on under the dash.
Most cars I have worked on only had about 4 bolts holding the seat down and maybe a plug or two. The LS might be a little different since there is an AC air outlet under the seat, so maybe you can't lay on your back there.
It sure saves my back when I have to get under the dash for long periods. In this case, hopefully you only need to be under there a few minutes and maybe you are small. Otherwise, pulling the seat is awful tempting and usually very easy.
Good Luck,
Jim Henderson