References: https://www.salesforcelwc.in/2019/10/lookup-in-lwc.html

Below is a reusable custom lookup component. The standard lookup component usage is advised, but if you need to bypass the current user's sharing and security or you need more flexibility then use this custom approach. This code is adapted from the above reference.

DEMO: https://forcetree-developer-edition.na147.force.com/s/custom-lookup

STEP 1:

Create the Apex Class Lookup, and the LWC component customLookup

STEP 2:

Implement the customLookup component created above, as shown in the example below.

This post shows how to use SOSL to fetch records and display using LWC.

Demo: https://forcetree-developer-edition.na147.force.com/s/datatable-sosl