Playing at home could indeed be quite profitable for Bayern Munich in the second leg at the beginning of next month, because Lazio, who only have one goal in the first leg, will definitely have difficulty preventing Bayern Munich from getting more wins at the Allianz Arena. Because on the one hand Lazio is also not a very good Italian team this season so it will not be that difficult for Bayern Munich to win at home in the second leg with a score of more than one goal.
Of course playing at home is a big advantage for a team, but for Bayern Munich they are currently experiencing a significant decline in performance in the last few matches so that is a possibility for Lazio.
If you look at the overall strength of these two teams, of course Bayern Munich has stronger strength, but I have a little doubt that Bayern Munich will easily beat Lazio in the second leg because of the problems they are currently experiencing.
For Tauchle, it is currently considered a failure to handle Bayern Munich with all the problems they are facing and the high possibility of retaining the Bundesliga title.
Tuchel is certain to leave Bayern Munich at the end of the season because he failed to coach Bayern Munich and it is even certain that he failed to defend the Bundesliga title. But against Lazio, I think this will be a game changer for his career at Bayern Munich. If he fails to make a comeback against Lazio in the second leg, chances are he won't have to wait until the end of the season to leave Bayern Munich, he could be fired.
Because as you said, the quality of Bayern Munich's players is above Lazio and the second leg was played at the Allianz Arena, so there is no reason for Tuchel to fail in the second leg, he has to work hard to turn things around against Lazio because this is a gamble on his career too. So, in my prediction, Bayern Munich will advance to the next round.