Liverpool can lose it's first position only if they show worst performance in there upcoming matches, which is not possible because Liverpool has lost just one game this season. Even if Liverpool lose 6 or more of it's remaining matches then Arsenal has to win almost all of it's remaining games, which won't be a piece of cake.
One main reason why Liverpool is Champions-Elect is that they are now out from all other leagues and there sole focus is now on winning EPL title. Arsenal once again has to bear second position in EPL if they play well in remaining games. The points gap between Arsenal and Nottingham is of just 4 points.
It's almost impossible because Liverpool will probably never lose consecutive matches in their next one so at this stage I think they will never be knocked off the top of the Premier League. On the other hand it is now crystal clear to us that Arsenal will never be able to top the EPL. Moreover according to the conversation you mentioned, Liverpool Football Club's sole goal is to win the EPL trophy. Maybe the Liverpool team has given their best in everything before but due to some of their weaknesses they may not be able to achieve that now. By the way Arsenal will definitely play well in the remaining games and they will face Fulham.