Hi @jja ,
Do you want to configure the Multiple choices LookUp field as a Searchable field as that in Person field in your Edit form?
Based on the needs that you mentioned, I think the ComboBox control could achieve your needs. Actually, when you generated an app based on your SP List which including a LookUp type column, the LookUp type column would be decorated as a ComboBox automaticlaly as below:

If you have enabled "Allow Searching" option for the ComboBox, you could type search text within the ComboBox to find the specific option.
If the "LookUp field" that you mentioned is a normal Text field, you want to configure it as a Searchable Multiple Selections field as Person field, you could consider add a ComboBox control within the corresponding data card to list available options, then set the IsSearchable property of ComboBox to following:
true
then you could type search key within the ComboBox to find the specific option.
Best regards,