Use the code below to change from the default equals comparison to the SQL LIKE operator for Lookup field data retrieval. The SQL LIKE operator checks if a value contains another value. Just change 123 to the ID of the Lookup field that you would like to use a like comparison for.

add_filter( 'frm_set_comparison_type_for_lookup', 'customize_lookup_value_retrieval', 10, 3);
function customize_lookup_value_retrieval( $type, $parent_field, $child_field ) {
        if ( $parent_field->id == 123 ) {
            $type = 'like';
        }
	return $type;
}