Pending approval from the Massachusetts School Building Authority, dreams of a new Pickering Middle School in Lynn and Saugus High School will be much closer to reality this week.The MSBA board of directors will vote Wednesday whether to invite the two projects into a 270-day eligibility period, marking the start of a years-long path to new school construction.”I am so grateful to the MSBA for recognizing our urgent need for new schools, and I am absolutely thrilled that we are being invited into the eligibility period with Pickering,” Lynn Superintendent Dr. Catherine C. Latham said Monday.Local educators have stressed the need for a new Pickering for the last two years, with Latham and School Committee member Charlie Gallo escorting MSBA officials and statewide candidates on tours of the school with its sagging ceilings and water-stained walls.Built in 1917 with a 648-student enrollment as of December, Pickering has been prioritized for replacement since 2007 by Lynn school officials along with Marshall Middle School. A new Marshall is being built with an anticipated 2016 opening. When the MSBA in December 2013 rejected an initial plan to replace Pickering, city officials drew up another plan they submitted last April.”The district is desperate to move Pickering into the pipeline because of the serious overcrowding that will overwhelm the middle schools in a few scant years and because of the seriously inadequate building that Pickering is,” the plan stated.Saugus officials last April also submitted a “statement of interest” proposing Saugus High School’s replacement to the MSBA. Construction on the existing high school began in 1954 with additions added in 1960 and 1972.”The building has now exceeded its 50-year projected life by a decade,” noted the statement of interest Saugus filed with the MSBA.The statement also notes that the high school’s “…design and layout are incredibly inefficient?””Our building is out of date and way too large,” School Committee Chairman Wendy Reed said.If Lynn and Saugus win MSBA approval to enter eligibility periods on Wednesday, they will begin to take the first steps toward – hopefully – winning eventual project approval and a commitment by the MSBA to reimburse them a portion of project costs.”The eligibility period assists the MSBA with managing its financial resources by identifying early in the process whether a district is ready to manage and fund a capital project,” according to the MSBA website.In an effort to drum up MSBA interest in replacing Pickering, Gallo shepherded then-state treasurer Steven Grossman around the school in 2013. Latham gave Deb Goldberg, who officially becomes state treasurer on Jan. 21, a tour last August. The state treasurer chairs the MSBA board.”Pickering is not up to par for learning standards – it is a facility that is way out of date,” Gallo said.The city’s statement of interest for Pickering describes how school guidance counselors work in “a closet ? with no windows and no ventilation” and how the school library was converted long ago into a classroom.In other business on Wednesday, the MSBA is scheduled to receive a formal request from Swampscott to withdraw its plan to build a district-wide elementary school. Town residents voted down the project last Nov. 4.