How are the outputs of multi-select questions saved in CommCare

Assuming your question is named /data/location_id_result, you can reference the name of the location selected with the expression

instance('locations')/locations/location[@id = /data/location_id_result]/name

and load that into a hidden value which you then save to the case.

If this is not a question completed by the user you should just use a hidden value with a calculate condition. The calculate would be:

instance('your_lookup_table_id')/your_lookup_table_id_list/your_lookup_table_id[index = #form/index]/study_condition

Where "lookup_table_id" = the id of your lookup table and #form/index you should just drag the index question in your form over.

Finally, be sure to include the instance statement in your form so it loads the lookup table you need. It should look like:

<instance id="your_lookup_table_id" src="jr://fixture/item-list:your_lookup_table_id></instance>