If it’s degraded you can keep playing if you like (although I know lag is annoying!). Most times it shouldn’t cause you to lose anything, if it lags out or has a never ending loading screen at the end of a battle, you can wait until it resolves to get your rewards.
If you have any concerns about the lag affecting your rewards though I would advise against playing Delves or Guild War battles for example where there’s limited battles.
Opening chests while there’s lag is completely safe.