Well, yeah. Basically, Lilly "defined" Sakura as a cat/magical girl's pet. The Enemy, which had changed the doll, turned tail and fled at the barrage of definitions. The Time Devourer itself was dead, but the "doll", made to come to a state of "unlife" by the Enemy's power, had become a husk of a cat. The procedure Death suggested and Lucas performed allowed for something benign to fill that husk, creating Sakura, a benign type of life with the purpose of helping Lilly become a magical girl, as defined by Lilly.
However, Lilly WASN'T changed into a magical girl by the Sun. So, Sakura will, instead, teach her magic the "old-fashioned" way. Which means that, where magical girls are "sorcerors" - magic runs in them, they cast innately - Lilly will be the first "wizard" of the new age - one who studies (and can teach!) magic so as to be able to cast it. In that sense, Lilly will be beginning to take steps on the new "field" her father is trying to conceive!
Sakura following the mores of a magical girl's pet, it also means she'll keep Lilly in the straight and narrow regarding magic and regarding everything else, and she'll be very careful about what kind of magic she teaches Lilly ;).
