My experience was years ago with (olds) Lexicon Lambda USB + a Presonus (don’t remember the exact model, but it had two inputs and outputs). Both do had (and still have?) good manufacturer’s ASIO drivers, I don’t talk about ASIO4ALL here, which is no use in this case.
The project was to record our amateur group live, so that listeners (possible contractors) could have a good idea of what it gives in reality.So no re-recordings / overdubs and no punch ins / outs, no cheating, the record has to be as authentic as possible.
So we mixed (with an analog mixtable) the bass in mono and drums in stereo on a mixtable subgroup directly connected to input channels 1 and 2 of the Lambda, and voice and guitars was mixed the same and connected to the 2 inputs of the Presonus.
We recorded the four tracks simultaneously on Cubase 6 on Windows 7 without any problem.
I remember though that we has little synchro issues during the final mix (always on Cubase 6), but nothing unsolvable, thanks to the possibility to finely offset tracks individually. The final result was engraved on an audio CD and served as our main demo during years, and no one ever complained about it. On the contrario, we had many positive returns concerning the quality of the recording.