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Yep they sure do make pressure treated LVL's, but for what your describing an LVL would be an inappropriate thing to use.
I agree with HayZee a 4x6" would be a much better size to use for a 24' shed.
Or
Like the captain suggested you could use 2x4 ACQ for example ---------2- 2x4x12' on each outside sandwiching 3 - 2x4 x 8' in the center all nailed or screwed together (that would be 7 pieces of lumber in total and it would in effect make a 4x6)
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