Journeys end with lovers' meetings

Journeys end with lovers' meetings
 

At the doorway of the Howe Street flats a man, muffled in a cravat and greatcoat, was leaning against the railing. He started as the hall-light fell upon our faces. "Holmes!" he cried.
"Why, Gregson!" said my companion as he shook hands with the Scotland Yard detective. "Journeys end with lovers' meetings. What brings you here?"
===================
The internet tells us the red words are from Shakespeare, but no explanation comes from it. What does it have to do with Holmes meeting a detective from Scotland Yard?

at last we meet

This is not a commonly used espression.

Since it's a supposed quote from a song where people find true love after going through a tough life, isn't it a slightly sarcastic comment on the encounter as if "true love" (the SY detective) came over at the end of the day/wait (journey)?

Thank you~