Naruto Manga has ended but there has not been any information about Itachi's lover. Kishimoto Masashi has not disclosed anything about Itachi's lover but some speculation can be made.
As we know Itachi, he entered Anbu at 11 and became captain by age 131. And the massacre of Uchiha clan took place while he was in Anbu. So his lover may be from Anbu and the highest possibility that she is an Uchiha otherwise Itachi would have not kill her.
Mentioning about Itachi's lover, Kishimoto might be trying to show how much Itachi loves his brother and give strong hold to the plot about Itachi's relationship with his brother Sasuke. Killing whole clan and his own love but not his brother does provide strong proof about how much Itachi loves his brother
I would like to mention about fan fiction here, as anime is progressing with lots of filler, within some filler there might appear Itachi's lover. As for the fan fiction her name is Aya Uchiha.