That reading seems hard to justify. The object *someone* in the construction "commit *someone* (to do something)" is realized in Japanese with the marker に in the causative construction "*someone*に約束/確約/etc.させる". (There are many other ways to translate "commit *someone* (to do something) of course.)
But there is no に-phrase in "レムにLを殺させることを確約させた月" that corresponds to "himself" in the proposed translation "月, who committed himself to make レム kill L".
For that translation to work, the source text would have to be something like "レムにLを殺させることを*自分に*確約させた月". It may be argued that "自分に" has been …