I also have an LH Senator card. Over the years I've had one upgrade from Y to C on a European service which was scheduled to operate with and A321 and operated with an A320, it was totally full and presumably they had to upgrade one or more people to get everyone on - but presumably not more than four or they would simply have moved the divider. Given the real differences between Y and C in Europe, I wasn't thrilled by it and I get in C class often enough anyway.
I have been upgraded from C to F on SQ a few times, most recently three weeks ago, always when the plane has been full, presumably because the card is also a Star Alliance Gold card but I must have been in the right place at the right time because they always upgrade their PPS and Solitaire card holders first if they need to upgrade. I actually accumulate most of my mileage on SQ these days but I doubt that they can tell that from my card.
One thing I have done that has worked sometimes when flying on Star Alliance carriers other than LH is ask in the lounge if it is possible to upgrade and pay with miles. I know it isn't at the moment but sometimes they will do it for good will if you spin a story of a long and tiring business trip.