the spies do not have to be Svaltalves. Did Harry have a spy in the White Court? Sure he did - Justine. The White Court didn't find her.
I find it really difficult to believe Lara wouldn't have predicted Thomas' lover would share information with him, and given that Thomas was closer to Harry than to the Raiths for a good part of the time since BR, anything that concerned him would probably have reached him. Lara isn't dumb, and that wasn't anywhere near as subtle a spy placement as Harry seemed to think.
Lara saw Justine as useful because she couldn't be whammied by anyone else in the court and would generally support Lara because Lara was looking out for her beloved Thomas, but I really doubt she was ignorant of Justine's allegiances. I think anything Justine saw was filtered through 1) does Lara mind if Harry sees it? 2) can Lara benefit from Justine unwittingly passing misinformation to Harry on this topic?
The latter may have been an unintended blessing, because while Harry actually didn't ask Justine for much out of concern for her safety, Lara was probably showing her enough disinformation as a precaution that Nemesis would have got a fair bit of fake mixed in with the real material.