With a lookup table, the first match will be the one that gets used.
In your scenario, if a customer has three products with different conversion labels, obviously this will not be satisfactory.
To solve this, you would need a custom javascript extension which checks each ProductId in the list, if there's a match, send the correct conversion event, then move on to the next one.
If you need any assistance with this please contact your account administrator or support team.
Many thanks
Steve Lake
Connecting data systems since the 1980s.