Scenes from the previous episode are shown out of sequence.
Goof: Although Lowell was definitely around when Joe, Brian, and Helen were growing up, and they may not have known who he was, they don't appear to have known him personally at the time (as Helen's comment "We didn't even know you then" in "This Old House" would indicate). It's hardly surprising that Brian would fail to recognize someone he hadn't seen in years who he barely knew in the first place.
Goof: Brian doesn't know who Lowell is, but in later episodes everyone seems to have been familiar with Lowell since they were children. In the second part of "Burnin' Down the House," Joe and Brian's dad refers to Lowell as the "Mather Boy" who Joe ran into with his bike when they were little. Several other episodes, such as "Remembrance of Flings Past" and "Miss Jenkins," even indicate that Joe, Brian and Helen went to school with Lowell.