Examples?

A single-payer healthcare system is your government mitigating the effects of your bad luck. Giving you a tax break for gains on certain kinds of investments is your government rewarding your work. (That's not traditional "hard work" in the sense of expending physical energy, but deciding what investments to make is certainly work.)

Well, I guess if "simultaneous" means that different parts of the government with different programs can have opposite effects, okay.

But I'm talking about a program that mitigates the effects of luck while (in the same program, with the same methods) rewarding effort.

They're mostly opposite effects and there's no way to reliably distinguish hard work from luck. That's why there's so much debate on the subject.

When I said "simultaneous" I mean to apply it to a government, not a particular program.

In any case though, any government program that gives equal resources to everyone and isn't means-tested to hell can do both. For example, an UBI both mitigates luck (by giving everyone a set amount of resources) and rewards hard work (because better workers will get far better returns with the income they've been given).

Sure, UBI doesn't completely negate the value of work, but UBI decreases the value of hard work because everyone gets something without having to do any work.