Within Salesforce Lightning, the ability to search Listviews was supposed to have been deployed in the Winter 19 release.
However, this search either is not visible or does not work within the Knowledge component.
I worked with Support and they led me to this Known Issue Link:
The link says that the Knowledge area simply does not have the listview search option but after speaking with Support, they said some environments don't have it at all and for others, it does not work. We fall into the latter category.
This request is for a working method to search only the Knowledge component of Salesforce.
Right now, a Global Search can be executed but this requires a number of extra steps and typically, an advanced search. It also makes searching Drafts much more difficult. Having a working option to search listviews would be extremely helpful.