NaOH reacts with carbon dioxide (CO2) in the air to form sodium carbonate (Na2CO3), also called soda ash or washing soda. The "lye lint" floating on your lye solution is sodium carbonate. It is insoluble in a concentrated lye solution, so it will remain as lint on top and/or settle to the bottom to form a whitish or grayish layer of sediment.
Strain it out if you prefer to do that, but IMO it is fine to leave it in the lye solution. It's the same thing as the soft white "ash" that sometimes forms on soap bars and it's the same thing as the washing soda that people buy to put in the washing machine for better cleaning.
When I use a masterbatched lye solution, I make sure the solution is well mixed before measuring some of the solution for a batch of soap. That way any soda ash is evenly distributed into every portion of lye solution I use, rather than some portions having more soda ash than others.
The most important thing is to store the lye solution in an airtight container once the lye solution cools to room temperature. Even when hot, I try to keep the container lightly covered at all times to minimize exposure to air. This will minimize the amount of CO2 and water vapor that the lye solution "sees". Concentrated lye solution will absorb water from the air as well as react with CO2 and you want to minimize both issues.