"It takes" doesn't sound natural to me, because "takes" is associated with length of time (for example, "it takes three weeks."). Even "it lasts" isn't so good a translation (nobody asks "when does it last?" but "how long does it last"--again, expressed in length of time). It seems to me that the most natural translation is "It runs from April to May."
I'd say all three -- lasts, takes, runs -- should be acceptable in the English sentence, because one could make a case for each of them.
But this gets Curiouer And Curiouser. I just discovered that if you click on a word in the "from sentence" (on this page), you get not just a list of the possible translations of that word, but also an example of usage.
For "trvá," you get... "Už to trvá hodiny" with the translation "It has been going on for hours." So much for "lasts, takes, runs"...
In a sentence like this, "runs" works fine. For example, "The Summer Shakespeare Festival runs from June through August," would mean that a selection of Shakespeare's plays will be performed from, say, 5 June until 20 August. (I will be glad to add "runs," if it works from the CZ side.)