Make sure all the score reels are resetting completely. Also, check the coin switches to make sure they are not stuck in the closed position.

Most likely a normally open switch is closed and it's sending power to the score motor constantly. Do you have a schematic for the machine? If you do, look for the score motor icon on the schematic and follow the circuit back toward the primary switches that send power to the score motor. Make sure these switches are clean and adjusted properly. If those switches check out okay, then we can look at secondary relays and switches that, in turn, open and close the primary switches...

You can check with other owners on Pinside who might have a copy of the Lucky Strike schematic:

https://pinside.com/pinball/archive/lucky-strike/owners

Also, you can check with The Pinball Resource to see if they have a copy of the schematic in stock:

http://www.pbresource.com/mansch.html