I haven't personally done this, and I'm just kind of spitballing here.

But if it would be acceptable to just obfuscate the information somewhat rater than fully hiding it, you could try something like this.

You can trigger a Data Lookup from the current user value without populating that value into a field.  On the Lookup Rules, instead of selecting a field for the "When" criteria, you can select "_(Current User)" which will allow you to lookup values based on the current user's username, but not in a way that someone could use inspect element to modify a field that contains that username to trigger a different search (or at least I don't think they can modify that).

That might be enough obfuscation for your purposes, triggering the lookup by the logged in user without needing to have that username stored in an editable field.

However, if you want additional obfuscation, you can use that lookup to lookup values from the cf_users table on your LFForms database.  You could return either user_id, which is an integer identifier for each user, or you could return the sid which is a long alphnumeric identifier for each user.  There is also an auth_code value in that table on version 11, but I'm less confident with how that value is used - so you'd need to do testing if you wanted to use that.

Returning one (or more) of those values to the hidden fields on your form, you could then use them to trigger secondary lookups (you could set-up Views on your own database that include joins back to the LFForms.cf_users table to facilitate those lookups), you've now got lookups that are using the current user, but with some obfuscation regarding what value is being used for the lookup.