You don't need to worry about the list of suppliers being sorted, just use a 4th parameter FALSE in the VLOOKUP statement.
i.e. If the invoice date is in column G and the supplier name is in column J (for example) and you have a worksheet of suppliers and payment terms (in number of days) in columns A and B, your due date formula for the invoice in line 2 would be =G2+VLOOKUP(J2,'Payment Terms'!A:B,2,FALSE)
This will work for a table of suppliers as long as you version of Excel allows (limited at 65,536 in Excel 2007 and earlier, now over 1 million). However it will slow your workbook down massively if you have thousands of invoices using this formula. So, say you never expect to have more than 1000 suppliers, change the A:B part of the formula to A1:B1000 and it should work faster.