The tie-breakers for Serie A are, in this order:
- points in head-to-head matches;
- goals scored in head-to-head matches*;
- goal difference;
- goals scored;
-draw.
* The "away goals rule" does NOT apply.
Because we won 1-0 in San Siro against Lazio and they won against us 2-1 on their turf, we are tied in head-to-head matches; so, if we are level on point, the next tie-breaker would apply, the goal difference.
As for the other point that was being discussed, there is one case (and one only!) where the position in the table in your league is relevant for the seeding in champions League: the clubs who win one the 6 leagues of the 6 countries with the highest ranking are in pot 1.
So real Madrid, Liverpool, juventus, Bayern, psg and zenit are in pot 1.
In any other case, the position in the table in the home league does not affect the European ranking and, as a consequence, does not affect the seeding for champions League/Europa League.