if that profile does not have access to the account object the lookups will be always empty (because that profile cannot read accounts).
Before continue reading, please note that I’m just discovering the sharing rules and all the things with not internal users, so the information can not be accurate or wrong.
I think you have 3 options here:
- Give read on accounts (and don’t share any account with that user / group so he can use the object, but no data is shared with him (I think a user has automatically shared the account of his/her contact). I don’t know how this will work if you try to put an account that is not shared with the user in the lookup, probably will fail (the record does not exist for that user)
- Use apex. I think apex does not look at the permissions in profiles,(I’m not really sure of this). you can store the data on text fields and with a trigger update the account, or schedule a batch to set the account in all the feedbacks without account
