Marlowe's misconduct - first and foremost- was , that in the spring of 1593 he was considered the author or contributor of the circulating leaflets ("libels") held in verse, signed with "Tamburlaine". (-> »Dutch Libels". one has to assume Marlowe wrote them). He was accused of high "treason", "rebellion" and "sedition", an accusation which was punishable by death. Queen Elizabeth must have regarded Marlowe as the initiator of the Libel texts. Influential circles should Elisabeth have asked to condemn him to death (not primarily - as commonly believed- because of Marlowe's atheistic heretical views). Without this background questions what motives could have prompted Shakespeare alias Marlowe to start his poetic work with the metaphor of Lucretia and Tarquin cannot be answered adequately.
The poem "Lucrece", Shakespeare's op.2 can be seen as the first literary creation of Marlowe after his life catastrophy under his new dramatist pseudo-name William Shake-speare *2). "Lucrece" is his acute metaphoric literary treatment of his serious misconduct towards Lucrece (the Queen) ...Tarquinius (Marlowe) had "tar"red the "queen".....
There is no way to explain how Shakspere could have read and known from Guilio Romano, from the untranslated poems of Ovids Fasti, from the poetic decription in "Lucrece" of The Fresco's in the "Sala de Troy" in the "Palazzo del Te" in Mantua.- Shakespeare must have beeen physically in Mantua to study the particular group of paintings.
*1) Picture out of Charles Sorel/John Davies "The Extravagant Shepheard"(1653/1660)
*2) "Venus and Adonis" Shakespeare's opus 1, was an earlier private commisioned work for William Cecil, for his ward Henry Wriothesley.