Whilst the official currency in the TRNC is the Lira, they will also accept the Euro and I believe sterling in some cases.
Whether you get a better exchange rate depends on where you change your money but here in the South many visitors find it easier to just bring a few euros for the first day then either use their cashpoint card to withdraw money or go to one of the many foreign exchange offices or the bank.
Remember that many parts of the TRNC are remote so you will only be able to change money in major towns like Girne (Kyrenia).