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The luck that Liverpool have is that they have already established a very good lead on the Premier League table so losing at this point is something that is going to be very difficult and impossible. Even if they don't do well, they will keep heading to win the trophy even if they draw games. This remaining side of the season should be a time for the Arsenal coach to plan for next season because his team definitely needs a lot of squad depths to be able to compete to win the Premier League. And the longer he stays without being able to win the Premier League the harder for him and the slimmer the chances for him to keep his job.
Liverpool are lucky, they tried hard and they managed to do it when the other competitors were not in their best form. Arsenal, Manchester City and others have gone out of the title race, so now Liverpool will just try to maintain their good performance so as not to lose points. The points gap with Arsenal is 12 points, that is a safe position that is already difficult for Arsenal to overcome.
In addition, Arsenal is a team that does not change managers often. They tend to keep one manager for a long time and this allows Arteta to be retained even if he fails to win the Premier League title. Arsenal is very different from Chelsea, Tottenham or Manchester United, meaning they tend to give the same manager a chance to try his best.