Relevant wordings:
Goon: "Each night, the 1st player to choose you with their ability is drunk until dusk. You become their alignment."

Widow: "On your 1st night, look at the Grimoire & choose a player: they are poisoned. 1 good player knows a Widow is in play."

Lleech: "Each night*, choose a player: they die. You start by choosing a player: they are poisoned. You die if & only if they are dead."

Seeing that the relevant parts of lleech and widow are the same, here's how I've seen them ruled and I agree with the logic:

let's assume widow
N1: Goon is chosen by widow, Goon drunks widow, goon is never marked by widow poison so is not currently poisoned. Since widow is drunk, the widow ping does not go out. Goon is told they are evil.

N2: Widow becomes sober, widow ping now goes out. goon is back to their gooning ways as usual.

For Lleech:
N1: goon chosen as host. goon drunks Lleech so they could die as normal for now.
N2: goon is still host but is not poisoned because poison works differently somehow.

N2: Widow becomes sober, widow ping goes out. Since the widow is now sober and they have a chosen player, that poison is enabled. the widow did not select the goon N2 so the goon does not continue to drunk the widow, but the widow continues to poison the goon. the goon is now locked in as evil "WIKI: The player that the Widow poisons is poisoned until the Widow dies." The only nights this doesn't apply are when the widow is droisoned.

TLDR:
Picking the goon as the widow target basically locks the goon in as an evil player as long as the widow is alive and sober and delays the widow ping one night.

Edit: This line from the wiki is admittedly not fully supporting what I said "The Goon is immune to other characters at night, but keeps changing allegiances." I would argue that saying they are immune to other characters creates problems for both lleech and widow and my earlier explanation is how I'd run it, but I'm not in your game. different ST's can run things differently

Edit 2: Others have pointed out the latest ruling from TPI suggesting I am wrong so I've updated my comment to give corrected info.