He had him tortured, and Marillion broke. Everyone does.
Marilion’s presence is a great example of Littlefinger getting super, super lucky, because if he didn’t exist Littlefinger would have had to create him, and Littlefinger clearly had no plans to.
Like, let’s look at the setup for murdering Lysa. Littlefinger had clearly been planning to do that at some point, but just as clearly hadn’t been planning on doing it so soon; Lysa was useful to him alive for much longer.
So let’s look at this setup. Littlefinger has been bragging openly for months and almost certainly privately for years that he had Lysa’s maidenhead, and Lysa is widely known to be unstable, flighty, prone to strong emotional outbursts she then follows up on. And part of the reason she’s known for that is that Littlefinger has been emotionally manipulating her for years to encourage those tendencies in her.
So Lysa is already established both as someone the Lords of the Vale don’t much care for AND as someone with a pre-existing romantic and sexual interest in Petyr Baelish, as well as someone who would do something super impulsive like marry him instantly the second she’s capable of doing so. Cool. This sets up Petyr as the eminence grise in the Vale.
It also sets him up as THE prime suspect if anything at all happens to Lysa. The upjumped coin-counter with a spurious claim to Harrenhal who is known as a silver-tongued cunning bastard that nobody really likes or trusts marrying so far above his station? Yeah, if Lysa dies everyone is gonna be looking at him. Everyone DID look at him! There was an armed rebellion that he had to dance really fast to get out from underneath.
So to get rid of Lysa, he needs a patsy. A convincing patsy. And he has, as near as I can tell, taken NO steps to set one up. Marillion’s presence is an enormously lucky break for him; a singer (already a suspect social class; randy, passionate, untrustworthy singers are practically a stereotype in Westeros) who has attached himself to Lysa’s entourage, who is roundly loathed by all the Vale Lords because he constantly mocks them and hides behind Lysa’s skirts, always near her. He didn’t arrange for that to happen; it happened without any input from him whatsoever.
Without Marillion, Littlefinger is in an awful, awful spot when Lysa has her final mental break. (There are many who say this break was deliberately provoked by Baelish creeping up on Sansa; I say bollocks to that, Littlefinger has enormously poor impulse control and likes to do flashy, unwise shit to prove how powerful and in-control he is, and he’s clearly been salivating to get his hands on Catelyn 2.0 for ages.) Lysa is babbling all kinds of ridiculously incriminating shit and threatening to kill Sansa, who is the key to all of Petyr’s future political and sexual plans, and without the enormously lucky break of Marillion standing literally right there, Littlefinger is in a CRAZY bad spot, because Lysa unspooling right in front of him also represents the unspooling of his plans (what if she has a similar breakdown in front of, say, Bronze Yohn Royce at some point?), and if he kills her without a patsy even HE probably can’t salvage anything from that.
Only the gods provided not only a patsy, a patsy that Lysa, again with no input from Littlefinger, placed right where he needed to be for Littlefinger to take full advantage.
Littlefinger is the luckiest goddamn schemer in all of Westeros.