When it occurred in our game yesterday, I was initially surprised that I didn't KNOW the answer. It must be the first time its ever happened in my 250-300 games!! That seems unbelievable to me, but there you go. We searchED here, CSW and BGG. There was a short thread on the Geek as you have posted, but that was more opinion than solid fact. In the end, we let the re-roll go ahead (and it missed) so nothing was changed either way. But it would be good to know the 'truth' LOL
BTW both answers have their 'hard evidence' to draw from.
The square rules state that no more than one dice can ever be rolled against a square (except combined arms). The lancer rules state they always re-roll flags in attack (except against cuirassiers) and does not give a square as an exception.
Q: Does a Lancer get a reroll against a Infantry in square, if he roll a flag with his die?
A: Yes - A lancer unit will reroll a flag when attacking a square (including flags of combined attack)
Richard Borg; 2018-06-24
So Richard´s intention here is, a Lancer reroll is not a "basic additional" die because of any cards e.g., but its a reroll of a battle result (flag symbol),
although the final result of the reroll can be an additional hit/retreat.