The phrase "assemble lists" is correct and usable in written English.
You can use it when referring to the action of gathering or creating lists of items, information, or data.
Example: "In order to organize our project, we need to assemble lists of all the necessary resources and tasks."
Alternatives: "compile lists" or "create lists".
For a game I call This or That?, I like to assemble lists of words or names or phrases that can fit into either of two categories.
Critics, on the other hand, assemble lists of Commonwealth failings.
(Salvadoran government documents were used by death squads to assemble lists of people to kill).
You have to assemble lists of donors and databases of voters to contact, and you have to develop a base of volunteers who can carry out the vital tasks of organizing and campaigning precinct by precinct.
While I could assemble lists of films on a given day to go see, being in my home city meant that it was pretty easy to prioritize other things, such as staying home to work on an assignment for an upcoming deadline.
Our first goal is to assemble lists of functionally related genes from such collections.
The aides furiously assembled "lists of early successes" on whiteboards.
Students in Environmental Science Communication at Pace University are assembling lists of vital online touchstones related to environmental science.
Dickson has previously assembled lists of word words in book books devoted to the specialised lingos of drinkers, soldiers, baseball players and American presidents.
Indeed, many advertisers are finding surprisingly good results by using companies that have assembled lists of people who have agreed to receive advertising by e-mail.
He'd assembled lists of email addresses for executives at companies that had done him wrong, and his notes to them had all led to resolution.
