Originally Posted by
jbmasta
The New 52 Green Lantern crossovers:
- Lights Out, involving all four Lantern titles (GL, GLC, New Guardians, Red Lanterns), available as a trade volume
- Uprising, a Green Lantern and Green Lantern Corps crossover (Green Lantern Corps Vol 5 trade)
- Godhead, all five Lantern titles (GL, GLC, New Guardians, Red Lanterns and Sinestro, plus a Green Lantern/New Gods one-shot), available as a trade volume
As you can see this period was relatively crossover heavy. For Lights Out and Godhead, my advice would be the event trades, which collect all the issues for the crossover.
DC You for Green Lantern doesn't have any crossovers. The Jim Gordon Batmech guest stars in issue #47 or #48, but it's a continuity-light and a brief guest spot (and yes, Hal makes the bunny ears remark about Batmech). Green Lantern Corps has a couple of six issue mini-series, Lost Army and Edge of Oblivion, which are good reads, however the writer on Lost Army didn't have as many issues to work with as he expected, so if you go into that don't expect any major resolution. The setting for those is the universe before our's, so that explains why Hal is pretty much the only Green Lantern around. Kyle was in Tom King's Omega Men 12 issue mini-series, but the only follow-through of that in Rebirth is Scrapps having a guest role in the Inhuman Trafficking arc of Green Lanterns.
In terms of one-off issues with Hal, there's the Green Lantern tie-in one-shot for Futures End, which as far as I know is only collected in the Futures End omnibus collection. You can get it on digital though, if you're just after that one issue. It's stand-alone. The other is the Green Lantern one-shot for the Justice League Darkseid War event. It's considered the best Hal material for the latter New 52 period, and is collected in the Justice League Darkseid War Power of the Gods trade. It's very much a character study, and you can glean all the plot you need from what's given in the issue.
Kyle joins Hal Jordan and the Green Lantern Corps in the second arc. The first arc is about resolving the Sinestro Corp threads from when that title ended with New 52 and bringing the Green Lantern Corps back into the picture.
The trades of HJ & GLC provide all you'll need. The first volume includes the Rebirth issue, which establishes the Sinestro Corp and the GLC returning to the rest of the universe.