"I'm going to Pepper City!"
Future Master Roshi's past is exactly the same as his main timeline counterpart's prior to August of Age 764. Until Age 766 He along with the rest of the Z Fighters were shocked That Future Goku died from a heart virus. During one of Future Android 17 and Future Android 18's rampages in Age 780, he is shown to be hidden in a submarine near Kame House, along with Future Turtle, Future Oolong and Future Puar. Listening to the news of the ongoing destruction, he was sure he could go out and challenge the Androids, but decided not to do so when Oolong, Puar and Turtle begged him not to go.
It is unknown whether he survived when Goku Black invaded Earth. Since it has been stated by Future Trunks that there's hardly any humans left alive in his timeline. However, it is possible that he did not survive as he did not make an appearance in the climactic battle with Fusion Zamasu when Future Trunks was gathering energy from the rest of humanity and when Future Zen-Oh erased everything from existence.