I have a database field that is calculated using a lookup table,

The lookup table has 9 rows and 10 columns, Currently it is stored in a table.

Is there a good way to add this to the business object?

Well...I guess I don't totally understand what you are trying to do...but there are a number of ways to consolidate that you may accomplish what you are attempting to do.  You can create custom field properties, you can also use a view and map a business object to a view which will pull that data as well.  I guess I need more information before I can give you a more direct answer.

I have a table that has three fields A,B,C for example. When the user changed A or B then I need to get the new value for C for the table. Can I put custom code in the C field to calculate based on those two?

Currently I am upgrading an app that does this through the form, basically performing the calculation anytime the user changes or clicks on any fields that may change A or B. I would like to move this to the BO.

Yes. This is the purpose behind a custom field.