If I select a lens, Ki should take into account the name and sites the Lens searches. It allows the Ki to search the narrowly defined lens without asking for further context. Custom Assistants can provide this context, however AFAIK Ki isn't available as a model for it, and sometimes it's not worth the hassle for it.
For my specific case, I have a Lens named <College Name>. It searches <college>.edu and <department>.com. If I ask Ki about on-campus dining using this Lens, it responds that it doesn't know what college I go to and to provide details. My college can be confused for several other colleges, and Ki will keep attempting (and failing) to get results for the other college, when it should know that it can't get it.