Useful experience from Evernote here.
It is handy to press DOWN ARROW in the search field to see the seven last search queries.
The supplementary feature is to have possibly save search query by RightMouseClick on the Lense icon (with the ability to name it). And use saved search queries by LeftMouseClick on the Lense icon.
+1 for these features. Same, coming from Evernote.
Would love to see this as well
If the history of the search queries could be saved, the history of the last N entries could be used for autocompletion to easily recall a recent search.
That is definitely something missing. The search engine of Joplin is great and searching notes is a big part of using Joplin.
While the current search does the job, it would deserve some polishing IMO.
A good reference for searching and auto-suggest is the Alfred App.
Writting this makes me think that an Alfred Workflow for Joplin could actually be a good workaround at first and you know what... GitHub - beet/joplin_alfred_actions: Handy Alfred workflow for interacting with Joplin 
This is however Mac only so not really a good solution for everyone.
Hello,
I'm a bit late on this subject but this would be a great feature.
On the UI side, once in the search box, using Up and Down arrows will enable me to navigate inside history.