There are indirect lessons that could be gained from The Last Lecture by individuals who did not have happy childhoods or did not have two parents in the home during their childhood. While their experiences would have been very different from Randy Pausch's environment, some of the points he made in his presentation would still be applicable.
Pausch was mentored by persons besides his parents. His first football coach, Jim Graham, taught him the importance of fundamentals, both in playing football and in addressing life. "You’ve got to get the fundamentals down because otherwise thefancy stuff isn’t going to work." Later, football Coach Setliff helped Pausch understand the importance of enthusiasm, as in attacking a problem with energy and without holding back.
Pausch cites other influential persons and experiences that were not directly related to his parents. He learned from coworkers, from his employers, from his students. He encourages his audience to maintain their "childlike wonder" - the motivation to work hard without allowing obstacles to stop you from achieving the goals your heart desires. He instructs his listeners to "never give up."
All those lessons can benefit all persons, regardless of the parental support they may or may not have had as children.