Although I know Manchester United played a very good match against Liverpool in the FA Cup quarterfinal, which was one of their best performances this season, that shouldn't have given us hope that Manchester United can play that well in their next match. Although Manchester United has players who, when they are serious, can play very well and win a match, sometimes their performances look like an academy team or a small team that doesn't know how to play football. For that reason, I don't trust Manchester United as much.
Manchester United did perform very well when facing Liverpool in the FA Cup yesterday, because this match was played at Manchester United's home ground so the game looked very dominant in possession of the ball. I'm also not sure Manchester United can win against Liverpool in the second match, especially since this match will be played at Liverpool's home ground. Manchester United will definitely have great difficulty in attacking, because Manchester United's performance still doesn't look consistent in every match and they always make a lot of mistakes, especially in Manchester United's back line.
The FA Cup quarter-finals were a knockout system, so there were no home or away matches, it would not be surprising because that match also continued into extra time so clearly, it was a knockout match. But if what you mean is their second meeting in the Premier League match, Manchester United and Liverpool will still meet in the Premier League match, not in the FA Cup. But in reality, in their second meeting in the Premier League match later, Manchester United will play at home and Liverpool will be the away team.
Also, in reality, in the first meeting between Manchester United and Liverpool this season in the Premier League match, in fact Manchester United managed to hold Liverpool to a draw with a score of 0-0 at Anfield. Therefore, this season Manchester United managed not to lose by Liverpool so yes, it looks like playing away might still be a difficult match for Liverpool later but indeed, of course Liverpool will still have a chance to win.