If in good shape, please donate instead. Otherwise, contact the LASAN Customer Care Center at 1-800-773-2489 for information on how to dispose of linens.
Use for as long as possible before disposal, and donate instead of recycling if the item is still in good shape. Even if they have stains/holes you can donate them to textile recyclers like Goodwill Industries.
Many Salvation Army stores, Goodwill stores, St. Vincent De Paul stores, and I:CO drop-boxes (in commercial businesses) collect rags and textiles for recycling. Call your local outlet and inquire about textile and rag donations.