Expedia's Ukraine accommodation database doesn't list any hotels in or around Lutsk.
However, Bukovel has some accommodations. It is 170 miles from Lutsk. Expedia approved accommodation options here are the Radisson Blu Resort Bukovel and Park Hotel Fomich.
While you are here in Lutsk, try and leave enough time to check out the other great attractions Western Ukraine has to offer. If you're a nature lover, be sure to explore Western Ukraine's mountains. In addition, you should visit a selection of its castles and fortresses. Common pastimes in this particular part of Ukraine include snowboarding.
If you have time before you say goodbye to Western Ukraine, visit Avanhard Stadium. You could stay at the Mir Hotel In Rovno.
If you are planning on arriving or departing via Lviv International Airport, you may like to stay at Ramada Lviv, or Nton, which are both close.