Why does an Account search not work in Lightning but does work in Classic?
A user attempts to search for an Account in Lightning by the Account's Name and no results are returned despite the user being able to access the Account. The same user performs the same search in Classic and the expected results are returned.
The Lightning Search checks against an object's Tab Setting on User profiles for what objects are searched against in the Global Search utility. If the object's Tab Setting for the User's profile is set to "Tab Hidden" then the object will not return results in search in Lightning.
Setting the object's Tab Setting for the User's profile to "Default Off" or "Default On" will allow the object to be searched for.
Salesforce Help Documentation: Global Search Results