Boy, there are definitely multiple schools of thought on this one. I've seen a lot of systems out there that combine simple code/description pairs like that into a single table with a "type" to differentiate them, and then look those values up using the code and the type. Me? I think that's great for a transactional system, but lousy for a DW solution. Make it as easy to develop against as possible. Strive to have as little explanation needed as possible for either developers or consumers.

When I've had lots of close to useless dimensions like that in a fact table, I combine them all horizontally into a single junk dimension table, which contains the permutations of the values. So from your example it would be:

TableName: DimCustomerCheck

CustomerCheckKey BKPaymentMethodID PaymentMethod BKTimeZoneID TimeZone

1 1 LockBox 1 Eastern

2 1 LockBox 2 Mountain

3 2 ACH 1 Eastern

4 2 ACH 2 Mountain

To populate the DimCustomerCheck table, you either pre-load it with all possible combinations, all theoretical combinations (if you don't trust your business users to tell you the real list of possible combinations!) or you put in a fairly simple ETL that pulls the distinct combinations from the source system and populates new rows as you go along. Then your SSIS lookup would just be based on the BKPaymentMethodID AND the BKTimeZoneID.

Hopefully I've understood what you were asking and presented you with a viable solution,