What did they mean when they declared "Etzba Elokim Hi!"?
Rashi and Ramban #1: They conceded that it was a Divine act.
Ramban #2 (citing the Ibn Ezra) 1 : It was a natural phenomenon, brought about by Elokim (in whom Pharaoh believed) but not by Hashem (the G-d of Yisrael (in whom he did not).
Rashbam: They meant that it must have been a natural phenomenon that had nothing to do with Moshe and Aharon. 2
See Ramban, who cites a number of proofs that 'Etzba Elokim' and similar expressions refer to acts attributed to Divine Providence. Moreover, the fact that Pharaoh no longer called the magicians to appear before Moshe indicates that they submitted to his superiority (Refer to 9:11:1:1).
Because seeing as they insisted on believing that Moshe and Aharon were magicians, if they were able to produce lice then there was no reason why they could not do so (Rashbam).
Why did they refer to "Etzba Elokim" and not "Yad Hashem"?
Rashi (in Rus): Wherever one finds the term "Yad Hashem", it refers to the plague of pestilence.
Ramban: They meant that this was a relatively small miracle on Hashem's part, and they mentioned the Name Elokim because among themselves, they never used the Name Havayah, only when they spoke to Moshe, since that was the Name with which Moshe addressed them.