Sirius and Lupin probably did recognize his patronus, but it would have come as no surprise that he loved Lily Evans -- they knew that already, at school.
And perhaps one of the reasons Snape hated Sirius so much was precisely that he would recognize his patronus.
I would think that that would be one of the first things Sirius said to Harry. “He’s just jealous that Lily loved your Dad and not him.” Especially during the scene when Harry confronts Sirius and Lupin at Grimmauld place.