A street on the boundary of Covent Garden in London, particularly notable for the Theatre Royal. By the 18th-century, when Pope was writing, Covent Garden had become a den of disrepute: brothels, taverns, theaters. In Epistle to Dr. Arbuthnot (1735), Drury Lane is the home of the aspiring writer who'll submit anything for publication and willingly submit to any changes to his work because he's desperate for money. Essentially, Pope thinks he's a sell-out and actively contributing to the decline of culture and morality.
"Nine years!" cries he, who high in Drury-lane,
Lull'd by soft Zephyrs thro' the broken pane,
Rhymes ere he wakes, and prints before Term ends,
Oblig'd by hunger, and request of friends:
"The piece, you think, is incorrect? why, take it,
I'm all submission, what you'd have it, make it." (41-46)