universe crossings pertinent to this: as far as I can tell. Not bringing up the ds9 ones or TNG's own tangental universe with Enterprise C. dates are not definitive but i believe close.
Prime Universe/Mirror Universe: 2256: Buran incident results in Prime and Mirror Lorca's to replace each other in their respective universes. Fate of Prime Lorca is unknown.
Prime Universe: 2257: Starfleet becomes aware that Defiant is going to be lost some time around 2268.
Kelvin Universe: sometime around 2256: Montgomery Scott begins transwarp beaming experiments, losing Admiral Archer's prized beagle. Possible universe incursion?
Prime Universe/Mirror Universe: 2257: Prime and Mirror USS Discovery replace each other in their respective universes. ISS Discovery is destroyed with all hands.
Mirror Universe 2257: Loss of the Charon.
Mirror Univrese 2257: Murder of Doctor Culber, a prime Universe individual within the Mirror Universe
Kelvin Universe 2258: multiple uses of red matter: destruction of Vulcan by artificially induced black hole, destruction of Narada by artificially induced black hole
Prime Universe 2258: Doctor Culber is rescued and returned to life from the spore network, possibly the strangest crossing yet.
Kelvin Universe 2258/Prime Universe 2387: The Narada crew and Ambassador Spock cross into/or create the tangental Kelvinverse by the events caused by the attack on the USS Kelvin. As previous manipulations of the past have not been shown to create such a wide-sweeping new universe, something special occured with this moment.
2256-2258 seems to be a very active time for hopping across the three main star trek universes. And those hops aren't always static in time. Discovery took a small leap forward when it returned to the Prime Universe. If Prime Lorca were go also find a way out, he might also be moving forward in time. He might also just be driven as a starfleet officer to do something about the doomed crew of NCC-1764 in a few more years, since so far no one has seemed to show a lot of concern about them.