I am a college student. Is it permissible for me to say that I was present at a lecture which I did not attend, with the knowledge of the supervisor, who in fact sometimes asks us to do this?.
It is not permissible for you to say that you were present at a lecture from which you were absent, because this is lying. The supervisor has no right to allow you to do that, because that is cooperating in sin and betraying a trust. Allaah says (interpretation of the meaning):
“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment”
And Allaah knows best.