Complex sentence: Their openness to lay-practitioners fit in with the Japanese modernisation of the Meiji restoration, which began in 1868, and in which Zen institutions began to give permission to lay followers to practice Zen.
Split into simpler sentences: Their openness to lay-practitioners fit in with the Japanese modernisation of the Meiji restoration, which began in 1868. Starting in this period Zen institutions began to give permission to lay followers to practice Zen.