How can I repent from lying about the reason for not attending the condolence gathering for my colleague's brother, after I told him I was traveling, when in reality other circumstances prevented me from attending?

The basic principle is that lying is forbidden (haram), and it is only permissible in cases of necessity. The use of "ma'areedh" (ambiguous statements) can be an alternative to lying. Whoever has lied must hasten to repent and resolve not to return to lying, for repentance erases what came before it.