I share a rented apartment with two others in Arlington, VA. We are the middle of an annual lease. All three of us are on the lease together with the rental company - (non of us are subletting from or to one another).

If one housemate wants to move out, the remaining housemates will start looking for a replacement housemate, and obviously if one is found quickly, everything will work out well for everyone.

But if a suitable housemate cannot be found by the time the housemate wants to move out, is that housemate legally obliged to pay their potion of rent for the remainder of the annual lease until a new housemate is brought in?

Or can they give a certain notice (say 60 days) after which the two remaining housemates are legally responsible for paying for the empty room until they have filled it with a new housemate?

It partially depends on the wording of the lease. But generally, in such situations, each lease signer is responsible in total for the terms of the lease. Therefore, one lessee cannot vacate early without the permission of the roomies AND the landlord. In fact the landlord may be able to overrule the roomies. The landlord may also have the right to approve a replacement roomie.

If the roomie does vacate early, they could be held responsible for the balance of the lease as long as a good faith effort is made to replace them. BUT, the remaining roomies would be responsible for the rental. They would not, again depending on the wording of the lease, be able to only pay their shares. They would have to pay the full rental or risk being evicted. They could then sue the roomie who left for their share.

Agree, if one moves out without other roommates permission, they will have to pay complete to landlord. They will then try to sue the other room mate for his share.