I mean, how hard is it for an Android to simply 'forget' about Sherlock Holme's mysteries, but not the character?
Well, if LaForge himself is into Holmes to any serious degree, he
would remember how the stories play out. With Data faithfully reproducing all of Holmes' antics, he'd merely become another NPC in the program, and the program would essentially cease to be interactive, a major blow to LaForge if
he is a serious Holmes fan.
It would be a really obvious solution, then, for LaForge to ask for an all-new Holmes mystery. LaForge just worded that request rather badly, assuming the computer could grasp the context. Which the computer generally is perfectly capable of doing; it only becomes a literal-minded moron when the plot specifically calls for this.
Although the very exchange you quote sort of rules out LaForge being a real Holmes fan.