You can set a field to auto-enter a "looked up" value from your price table. This field need not be visible on the current layout, so you can hide it from the user but still use it in calculations.
You link your two tables via the Finishing type fields that are defined in each table. You define a "piece price" number field in your line items table and set it's auto-enter option to copy the PerPiece price from your FinishingOptions table.
On a design note, it very likely that you could combine all your types of service prices in one table. This may simplify the design of your Line Item table's record by quite a bit.
Typical table structure looks like this:
Invoice(or Job Estimates) -----<Line Items>-----Products/Services
You place a portal to Line Items on your Invoice layout and define a unit price field In Line Items to look up a price from the Products table.