The teenager, handed a rare start, justified the decision as the Gunners strengthened their grip on the Premier League title race.
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Lewis-Skelly, previously used mainly as an inverted left-back, showed his quality in a more central role during just his third league appearance this season with Arteta praising his patience despite limited opportunities.
"Because probably I don't have a clue. Maybe I should have done it earlier, I don't know," Arteta said.
"It was a big risk because I knew what was going to happen. If it works it's great, if we'd have lost the game - 'How do you play a kid at this age in this scenario in a position he hasn't played?' I knew that but I had the feeling it was the right game for him."