If you took a lump sum distribution while you lived in WA state, then that lump sum amount would be attributed to WA because that is where you lived at the time of the distribution and nothing to another state where you lived during another part of the year. None of it would be taxed by another state.
If you took monthly payments from the 401K, then you would allocate the amount between WA and the other state by the number of months you lived in each one.