Lacazette has missed Arsenal’s last two games with a hamstring injury while Tierney has been suffering from a knee problem.
The Gunners trail 2-1 following the first-leg against Unai Emery’s side in Spain this week, with their chances of European football next season hanging on Thursday’s game.
Both were absent from Sunday’s trip to Newcastle – for which Arteta made eight changes from Thursday – and the Gunners boss said neither had trained with the squad yet and would likely miss the next “few games”.
“They haven’t trained with us yet so it is very unlikely to have them ready in the next few games,” Arteta told Sky Sports.
Asked about the eight changes, the Spaniard said: “It’s just to prepare for today’s game the best possible way. We played 40 minutes [against Villarreal] with 10 men and we have had a crazy schedule.
“We know the risks we are taking every week. Last week we took the risk with Lacazette and we lost him. We need fresh players.”
Captain Pierre-Emerick Aubameyang made his first start in almost a month at Newcastle having suffered from malaria.
“He has been progressing every day,” Arteta said of the striker. “Against Villarreal, he could only play 10-15 minutes. Let’s see how long he lasts today.
“It is all about getting momentum and confidence, and winning helps. We have had some disappointing results in the last week or so, for different reasons, and today we need to win for the team to benefit.”
Dani Ceballos was sent off just before the hour mark on Thursday and will be suspended for the second-leg.