The 1 V is officially supported by LineageOS. Installation instructions can be found here.
EDIT: I will add that support for this device is quite recent, and it is still very expensive even second-hand. You are relying on a volunteer maintainer who makes no commitments about how long they will support the device for, so I think it's financially risky to buy the device purely based on it having LineageOS support now. You might want to consider the Xperia 1 III, which is two years older and significantly cheaper on the seocnd-hand market, but is otherwise quite similar to the 1 V. It has also received official LineageOS support for a longer period.