CustomerAddressType <---Store Types "Branch Location" "Billing" here to be used
There is nothing wrong with having an address type table and storing the type PK in the customer addresses table (e.g. "2" rather than "Billing"). You can also use this type table as the row source for a form combo and store the PK in customer addresses, or the string value if you prefer. The advantage to the former is that IF you change the string value for the type, the fact that the value in customer addresses is the type PK (e.g. 2) then changes to the value are of no consequence because you are using the record ID rather than the string.
The advice you were given regarding table lookups was about not creating lookup values at the table level. While you will see "Billing" in the table field, the real stored value is the number that Access has assigned to it - same as if you had done it yourself as part of good normalization practice. The difference isn't only that you can't upsize a db with such tables, it can make what should be simple queries or recordset handling require workarounds.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.