There is no difference. Both sentences are using the future tense to tell us that the tree's length will be doubled by summer.
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tashiroMy grammar book says the first sentence means the tree suddenly doubles in height on a certain day and the second means the tree gradually doubles by a certain day.I can't judge because it's not clear, in view of the rest of your post, whether you're talking about the tree or the lizard!
Is this explanation right?
tashiro