There is a gap in time, which would have given Dexter time to find out where she was -
Lila was not in a hotel - it's an appartment. Notice that she opened the door, and checked her mail - receiving the postcard with Doakes' picture on. The mail came through the door - in a hotel it would have been at reception.
Also, in the mail was a letter addressed by hand - inferring that she had been in Paris long enough to have been in contact with friends, one of whom had written to her.
Add up those facts, and Lila has moved to Paris and found an apartment - all of which would make her traceable to someone like Dexter - she probably never dreamed he would follow her there - much less to find some closure in his ongoing search to live in his own skin.
What a wonderful series - roll on number 3.