No, you won't be able to. I recently (this past weekend) flew on an itinerary starting on United (just a domestic segment) and continuing on Lufthansa and when presented with an offer to upgrade - 20,000 miles and $550 co-pay, only the United segment was eligible - the Lufthansa flights were not. However, there is one exception - if you book classes B or Y, you can use the Star Alliance Upgrade option and upgrade with miles. Other than that, you're out of luck. Sorry.