In fact we can go further with Monitor Brother scaling. In The Unexpected series, the titular group of heroes travel to the Monitor’s Sphere and confront Mandrakk the Dark Monitor. Yes,
the same one from Final Crisis that fought the Thought Robot. Despite being able to shake the entirety of Nil and his battle with the Bad Samaritan threatening to destroy the entire Monitor’s Sphere, heroes like
Hawkman could take Mandrakk on directly,
deflecting his attacks and surviving numerous blows from the vampiric anti-god. And retroactively, Death Metal had Darkseid’s fall in Final Crisis ripple into the Monitor Sphere. During the Perpetua saga preceding Death Metal,
the Anti-Monitor dominating a fusion with both his brothers, amped by the Totality, and having repossessed the Anti-Life Equation at a state he describes as the most powerful he’d ever felt was defeated by… John Stewart ramming him with The Flash’s car. ‘Cause comics. While you could argue the car was juiced on Speedforce shenanigans,
John himself is damn near the epicenter of the explosion so he’d likely scale to a portion of it anyways.
The third chain scaling would be Kyle being comparable to New 52 Anti-Monitor via the Life Equation, who’s able to directly fight an amped New-52 Darkseid, who Yuga Khan was comparable to when Darkseid was younger. Yuga Khan had the power of Shazam and with it, outright punched a hole through the Source.
Shazam at this time was powered by several Old Gods, which allowed him to be able to beat Yuga Khan. Anti-Monitor was able to
beat Darkseid with the Anti-Life Equation, and the Life Equation is equal to it. To tldr: Yuga Khan =< amped Darkseid < Anti-Monitor with ALE = White Lantern Kyle with LE. For further support, it’s heavily implied that Mobius, the Anti-Monitor’s original state before he found Anti-Life, is
still stronger than “God of Gods” Shazam who beat and added Yuga Khan to his power,
yet Steve Trevor of all people with the ALE just 1-shot Mobius shortly after he received it. So Kyle with more experience using the Life Equation should easily compare to and surpass Steve’s usage of it.
In conclusion, Kyle with the White Lantern Ring and Life Equation, has avenues to scale to characters from the Godsphere, Monitor Sphere, Sixth Dimension, and The Source respectively, which all depend on how high you have each in a cosmological scope. No matter what though, Kyle, with the Life Equation, can interact with and affect a part of the DC cosmology that shares an R>F transcendence with its lower denizens, as the Godsphere, Monitor Sphere, and Sixth Dimension are
fiction;
nothing,
but a dream of the Source, granting Kyle also
Outerversal levels of power, as the Life Equation makes up part of this Source alongside the Anti-Life Equation, both of which are two parts of a whole that they can consistently affect in its entirety, with
various actions affecting everything up to the Source itself, such as the Crisis on Infinite Earths causing a crack in the Source; said examples are things Kyle should be comparable too.