What is the definition of "solipsized?"

It's just a quirk of Nabokov's phrasing that the most accurate rendition in English relies on ad-hoc "verbification" to succinctly capture the sense more easily expressed in Russian.

From Bloom, 1993 - selection of literary criticism focusing on Vladimir Nabokov's controversial character...

It is a measure of Humbert's perspicacity that he is sufficiently aware of what he is doing to say that "Lolita had been safely solipsized";
the Russian translation makes the point even more bluntly: "Real'nost' Lolity byla blagopoluchno otmenena," which means, literally, "Lolita's reality was successfully cancelled"

I assume the intended sense is "Since Lolita isn't real, I can do what I like with her". It's a rather obscure philosophical context, so it's no surprise few Anglophones have found reason to promote this particular "credible, but unlikely" verb usage.

In practice (and somewhat less metaphysically) we tend to base this kind of rationalization on "Since [victim] isn't human, I can do what I like to her/him/it" (we dehumanize the victim, rather than philosophically rationalize her into complete "non-existence").

I think there is a simpler answer.

Humbert wanted Lolita to withdraw from any interest in the outside world and instead become more interested in her own needs and wants. This way Humbert would not have to worry about interference with his "sexual dance" from any authorities and the like, who they would come into occasional contact with as they traveled.

Solipsists were known to question whether anything outside the observer's mind really existed. This invariably led to the elevation of the person him/herself and not of those in the world outside. Solipsizing, a word the Russian writer Nabokov and lover of the English language apparently formed himself, seems to be a method used by Humbert of drawing Lolita into herself so that the protagonist could subsequently have even more control of her limited external experiences and hence participate in his "marriage" rather safely.