These kinds of observations have frequently been made for lensed quasars. Quasars are fairly stochastic and have random bursts in their brightness. If you see multiple images of the same quasar, you can see one of the images get brighter and then some time later (usually of order days) you can see the other image get brighter.

By measuring the time delay and the separations between the images you can get an estimate of the Hubble constant.