The question was raised by Joe F. in a previous thread, 11643 (linked at top). No one seems to have a copy of the first printing of the poem, so I am safe in posting this explanation.

Kipling was 3 1/2 sheets to the wind when he wrote the poem long after he left the scene of his youthful indiscretions and confused east with west. When he sobered up, he sent it off without proof-reading. After it came out, an editor happened to look at a map and changed it to lazy. 'Lazy' reads better than either eastward or westward.
The editor considered other changes, such as replacing her 'little banjo', which made the poem sound like something done by Foster when he was in his cups, with an 'ukulele, but gave that up since Kipling's writings were unlikely to survive to another edition anyway.