Not sure you caught the edit where I try to work through the fight. But here it is...
So like, if the Doc decided to use the Eye of Harmony to rewrite the laws of reality to benefit him and/or hurt LM, and weaponized the Heart of the TARDIS (essentially, the entirety of time and space converted to a power source) to use against LM, and managed to make the fight take place in some pocket dimension or abstract dimension outside LM's primary influence, whose properties level the playing field, or maybe the "un-space" between dimensions that is outside causal control...maybe we're getting close? But that also assumes a lopsided view of the fight, with LM doing nothing while the Doctor brings his best weapons to bear.
It would also be out of character for the Doctor, so we'd have to assume CIS is off.