The two sentences are both correct, but they have slightly different meanings.
Die wohl dickste Lüge lautete, dass die Person der Star einer Rockband sei.
The lie, that probably is the biggest, says, that the person is the star of a rock band.
The phrase »die wohl dickste Lüge« is one part of speech. It is a Nominalgruppe or Nominalphrase (nominal phrase), and this hole phrase is the subject of the sentence, so this group occupies only one position in the sentence (position 1), and therefore the verb (»lautete«) is where it has to be: on position 2.
In this phrase the adverb wohl (probably) modifies the adjective dickste (biggest). This adverb is not bound to the verb!
Wohl lautete die dickste Lüge, dass die Person der Star einer Rockband sei.
The biggest lie says probably, that the person is the star of a rock band.
Here the word »wohl« on its own is a part of speech that occupies position 1. It is an adverb that modifies a verb (which is at position 2).