Meyer lemon is a hybrid citrus fruit native to China. It is a cross between a citron and a mandarin/pomelo hybrid. It was introduced to the United States in 1908 by the agricultural explorer Frank Nicholas Meyer.https://hort.purdue.edu/newcrop/morton/lemon.html. The Meyer lemon is easily reproduced by rooting large cuttings in the nursery and planting them directly in the grove. The main advantage of the Meyer lemon that they fruit 2 to 3 years sooner than budded trees and have a long life, remaining in full production for over 30 years, perhaps much longer.
Back to the main question on how long does it take for a Meyer lemon tree to produce fruit, it depends on how grown from. A Meyer lemon plant grown from seed usually beginning to fruit in four years yielding thousands of lemons over its lifetime. Meyer lemon trees that are a product of grafting to a dwarf rootstock can start blooming as early as 1 year. https://en.wikipedia.org/wiki/Meyer_lemon