my first question would be where did you hit him?
I've noticed that firing AP rounds into "soft" targets like halftacks often will do nothing at all since I presume the shell passes right through it and doesn't hit anything critical. I'm not sure how much armor the lvt has off hand but it's not much so the above scenario is possible.
Also internet connection can play a part I've hammered enemy gv's to no avail because I was lagging a little.
At point blank range a M8 should be able to kill an LVT if you hit it in the crew compartment in just a few shots.
I should also note that this is all a lot of guesswork on my part. I do not drive the M8 often as I have a nasty habbit of tipping it over.
And I don't engage lvt's often with other gv's very often. So there is a lot of generalizations to what I'm saying here but some of it holds true.