Did the Virginia State Legislature vote to allow West Virginia to leave?
Yes.
The counties of northwestern Virginia had no interest in secession, being of strong Union sentiment. While the state government in Richmond was pondering a decision to leave the Union, the political leaders of those counties met in Wheeling to discuss the formation of a new state. But as Virginia had not officially seceded, there was a reluctance to move forward. When the voters of Virginia gave their imprimatur to secession, the counties of the northwest voted strongly against it. A second convention in Wheeling in June 1861 declared the secessionist government of Virginia null and void, and the members of the convention elected their own government which was quickly recognized by the federal government. Now there were two state governments for Virginia, one Union and one Confederate.
The convention decreed a statehood election for October in which the residents of 16 northwestern counties voted overwhelmingly for statehood -– in those areas occupied by federal troops. In other areas, the vote went against statehood, or there was no vote at all, as the county governments were loyal to the Confederacy. A state constitutional convention met in 1862 and asked for admission to the Union as a new state. Lincoln was willing to grant this -– provided West Virginia gradually abolish slavery. As to the constitutionality of creating this new state, Lincoln recognized the Union government of Virginia to be the state government that gave permission for the creation of West Virginia from its territory. In 1863, West Virginia became a state.
Following the Civil War, Virginia sued to undo the creation of West Virginia. Congress, at the same time, passed a joint resolution endorsing the creation of the state, and in 1870 the Supreme Court agreed.