Due to the search(lookup) restrictions in Kintone, you can only search by a word. It does not search for partially matching search keywords as mentioned in the following page:
Using the Search Bar: Precautions When Entering Search Keywords(this search rule applies to the lookup too)
As of now, if you are considering creating a JS to resolve this issue, a method that I can suggest is the following:
1. Using the REST API, get all records information (may be easier if you can specify the field or filter at this point)
2. Put the specific field information from the obtained data into array.
3. Use the JS function (such as "match" or "indexOf") to search
4. Obtain the key item from the search result and put into array.
(Repeat 3 and 4 until the records are gone)
5. Using the array information created from the step 4., create an URL query
Or you can simply recreate a lookup field yourself.
I hope this helps!