CAMBRIDGE — There were pompoms, college coeds in frilly dresses and leisure suits, and giant letters spelling out “LSD” tied to the balcony. And that was just in the audience.  It was a homecoming, after all. When Lake Street Dive performs in Boston, it’s an event. The quartet got started here a decade ago when its members met at New England Conservatory. With their soulful spin on 1960s pop underscored by their jazz sensibilities, they sharpened their hooks in cozy places like Club Passim and Toad before half the band moved to New York.  But it was only this year, bolstered by an acclaimed new album, “Bad Self Portraits,” that their destiny caught up with their talent: Lead singer Rachael Price, guitarist-trumpeter Mike Olson, upright bassist Bridget Kearney, and drummer Mike Calabrese became stars. Finally.  “We had an incredible year, the best that we’ve ever had as a band,” Price said Monday at the Sinclair, the first of three sold-out nights there.  It was familiar territory: Lake Street Dive sold out the Harvard Square venue in February, too, followed by buzzed-about appearances at Boston Calling and Newport Folk Festival.  Big things are also brewing for the new year. Price mentioned Lake Street Dive will be recording another album soon, and gave a sneak preview of some new songs. They were meaty, muscular compositions, with a surprising amount of tension and detours in the bridges. On one written by Olson, which the set list identified as “God Awful Things,” Price savored the word play in the chorus: “So thank the good Lord/ For the godawful things/ That brought you to me.”  And now a moment to admire Price’s poise. From the coy body language to the flawless vocals, she never loses control yet clearly gets lost in the music. That’s rare. In her hands, ballads become soul exorcisms to cast out demons – and deadbeat lovers. “It feels good to be over you/ But it felt good to be under you,” she practically purred on “Hello? Goodbye!”  A Twitter contest yielded a homecoming king and queen from the audience, with Price crowning them onstage with sashes. She and Jesse Dee, the homegrown soul belter who opened the show with flash and finesse, then serenaded fans with a cover of Ben E. King’s “Stand by Me.” It was a fitting gesture to a room full of folks who had done exactly that for Lake Street Dive.
Lake Street Dive, the irresistible Boston-bred pop band that finally broke out in 2014, comes home for a run of sold-out shows at the Sinclair.