Marvolo
Avenger
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That was partially explained already, though through interviews rather than the movie itself-- The map isn't specifically to Luke, it's to the first Jedi Temple.... Which is where the people that knew him best believe him to be. The portion of the map that the First Order had (from the old Imperial Archives) was also in Artoo, thanks to his jacking into the Death Star computer in ANH.
Don't know how Lor San Tekka got his part of it, but I believe his backstory is that (as well as being a leader for one sect of the Church of the Force) he was an explorer or archaeologist. So maybe it was him who helped Luke track down the Temple in the first place?
The Visual Dictionary says of Lors,
As the Empire toppled, retreating Imperial Officials destroyed records that would have been vital to the New Republic's attempts at galactic reconstruction. New Republic bureaucrats turned instead to firsthand accounts from well-traveled locals to fill in the gaps. A seasoned traveler and explorer of the more remote fringes of the galaxy, Lors has proven his worth to the New Republic and the Resistance many times over.
In his travels, Lors San Tekka uncovered much of the history if the Jedi Knights that the Galactic Empire had tried so hard to erase. Others now seek him for his knowledge of Jedi Secrets.
It also says that the map is stored on an antiquated storage device.
So putting it together, at some point in Lors travels during his life, he found the old storage device with the map to Ahch-to. After the Empire fell, Lors helped the New Republic and Resistance. Leia and him worked together and had dealings. They were possibly friends based on the way Lors talks to Kylo. Luke was drawn to Lors for his knowledge of the history of the Jedi. At some point after ROTJ Lors showed his portion of the map to Luke, and R2 found the rest of the map in his data banks from when he linked with the Death Star. They put the map together showing Luke the way to Ahch-to. After Kylo massacred Luke's Jedi Academy, Luke went to Ahch-to. R2 and his portion of the map went to Leia. Lors kept the other portion of map that was on the storage device.