Your lease should allow for you to enter the home on proper notice. You can sell the home with a lease, the new owner woudl just take subject to the lease. Talk to a local attorney about options such as suing for breach of lease or eviction, which may or may not be allowable.
The RLTA governs. Check it out at : http://apps.leg.wa.gov/RCW/default.aspx?cite=59.18.
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Be sure to have your management and/or agent give at least 24 hours' advance notice of your intent to enter to show the property. That is all that is required. Best practice would be to have that notice be in writing so you can show your due diligence to a third party, such as a court. If the lease is over at the end of May, also review your lease to determine what happens when the lease ends - do you have to give notice to end the tenancy, or does the tenancy become a month to month by default, or . . . ?
To answer your header, as the owner you can sell the property - subject to the lease agreement - and the tenant will simply have a new landlord. You need to advise the tenant where they should send the rent so there is no confusion.
Hope this helps. Elizabeth Powell