Apparently there's something called "anvil crawler" lightning that can work its way across a cloud.

https://en.wikipedia.org/wiki/Lightning

https://en.wikipedia.org/wiki/List_of_lightning_phenomena

Anvil crawler lightning, sometimes called spider lightning, is created when leaders propagate through horizontally-extensive charge regions in mature thunderstorms, usually the stratiform regions of mesoscale convective systems. These discharges usually begin as IC discharges originating within the convective region; the negative leader end then propagates well into the aforementioned charge regions in the stratiform area. If the leader becomes too long, it may separate into multiple bidirectional leaders. When this happens, the positive end of the separated leader may strike the ground as a positive CG flash or crawl on the underside of the cloud, creating a spectacular display of lightning crawling across the sky. Ground flashes produced in this manner tend to transfer high amounts of charge, and this can trigger upward lightning flashes and upper-atmospheric lightning.[1]

But in the video I see of it, while it's sustained by lightning standards, it all looks much shorter duration. This video is titled "Epic 3.72 second anvil crawler lightning", so over a minute seems unlikely.

Are you sure that it's not an aircraft, maybe illuminated in one way or another (e.g. a break in the clouds in the distance letting sun illuminate it directly, maybe?)