The Gunners moved closer to being crowned champions of England for the first time since 2004 following a 1-0 win at West Ham on Sunday but only after the hosts had a stoppage-time equaliser ruled out following a lengthy VAR review.
Victory left Arsenal five points clear of second-placed Manchester City, with two games to play - at home to already-relegated Burnley and away to Crystal Palace before the Gunners face Paris Saint-Germain in the Champions League final on May 30th.
"We have to stay humble," said teenage rising star Lewis-Skelly, now back in Arsenal's starting line-up after spending much of the season on the sidelines.
"(The dressing room is) just joy, excitement, fulfilment - everything you can describe," he explained. "We are buzzing, but we know that the job is not done.
"We have got two more (domestic) 'finals' (against Burnley and Palace) left now, and we have to take each game as it comes. The next one is Burnley - and then we go on from there.
"As players, as a fan myself, it's easy to think about what could be. But, it is important that we stay in the moment. We have to stay on it."
Lewis-Skelly enjoyed a breakthrough campaign last season but struggled to secure a place in Arsenal manager Mikel Arteta's side until he was given a chance against Fulham earlier this month and he has started every game since.
"It was tough initially," he said.
"But, for me, I pride myself on having mental strength. Sport is not one pathway, because there are ups and downs. And it's how you bounce back from that, and how you are in those moments when you face adversity. That is what defines you.
"I spoke with my family and friends. I just told them, 'I don't want to hear all the noise that is coming from social media. Let me stay in this moment, let me continue to face this adversity and let me come out the other side of it'.
"He (Arteta) told me, 'You are going to play in midfield, so go for it'. So, that is what I did. And I had to be bold and play with courage, because that is what this league demands," he added.