I currently use an HP EliteDesk SFF (the middle size one) and use a DAC for DisplayPort to RCA.

DACs generally add less than 1 frame of lag. Youre thinking of scalers. If the adapter applies any sort of processing other than simply converting from digital to analog, then it adds more lag. But simply converting will usually have nearly imperceptible levels of lag. I can try to measure it when I use it next and see, but I can say that I don’t notice any “awful lag.”