Things aren't adding up with Burt...
In episode 5 oBurt claims he didn't retire but was in fact fired for developing an emotional relationship with innie Irv at work. It seems unlikely that Lumon would tell his Outie about the romantic entanglement if it didn't need to - too many follow-up questions. Also, would sensual head contact really be a fireable offence if iBurt is such an important employee? Why wasn't Irving also fired, or at least why didn't he have the issue raised to him (Maintaining team chemistry for Cold Harbour could be an explanation?)
We saw oBurt record a retirement video - which would have been totally disingenuous if he was actually fired. He either retired or was fired - it can't have been both. I'm going to assume the retirement was an actual retirement.
From the night of the ODC there is one huge loose end for Lumon - what happened with Irving. They know he lied to Milchik about what he was doing that night, confirming he is antagonistic to Lumon. From Lumon's perspective, they'll be thinking: what would innie Irv have done? My guess is Lumon have made contact with Outie Bert to try figure out what outie Irving is up to. They are using their innies' emotional connection to lure Irving to dinner under false pretences..
The Walken factor aside, isn't it strange that Burt has invited Irv to a dinner to smooth things over? It seems like oBurt's natural first reaction would be to maintain distance as much as possible to smooth over his relationship with Fields, rather than say - I'm going to track this stranger down and invite him to dinner with my fuming husband. Lumon is involved.
There's a major twist on the way here, and I can't help but feeling the usually crafty oIrving is walking into a trap...
[Variant of this theory: the retirement was actually Innie Burt permanently replacing his outie, though the pre-existing relationship with Fields probably precludes this. I also think retirement is a genuine option, even for Lumon.]