OLYMPIA — The 105-day legislative session in Washington state begins Monday, and lawmakers return to Olympia this year with a variety of costly issues on their plate — including finding money to improve the state’s troubled mental health system. For the first time in years, lawmakers are set to write a new two-year budget without the primary focus being satisfying a court mandate on education funding, though they say there’s still work to be done to continue to improve basic education. Leaders in the House and Senate will release their budget plans in the coming months and will work in the coming months to negotiate a final budget before the session concludes at the end of April.