As long as you're purchasing a fare that's elligible for Star Alliance upgrades, on a Star Alliance carrier that participates in Star Alliance Upgrades, AND there's available reward inventory for the flight you're on, then yes, I believe your in-laws can upgrade you using their miles.

However, that last caveat may be the big problem for you. Star Alliance uses the same "fare bucket" for reward seats and for Star Alliance upgrades. So if you can't see a reward on the flight you're on, an upgrade will likely not be available.

The exception is the possibility that more seats will become available shortly before departure -- Lufthansa, for example, often makes business and first rewards available 14 days before departure. In that case, if you catch it quickly, you should be able to upgrade.

(Or, if you're on a fully-refundable ticket, as it largely required to get a *A upgrade, you can at that point book yourself the reward fare in the class you want, and cancel your revenue ticket for a refund.)