Do all anteaters lay eggs

It bears a single offspring after a gestation period of 190 days, which will stay near the mother until she becomes pregnant again. The baby spends much of the first part of its life riding on its mother's back, until it is nearly half her size

The Spiny anteater, more correctly known as the echidna, does lay eggs but it is not an anteater - it is a monotreme, and is completely different from regular anteaters (like the Giant anteater). Regular anteaters are in the family Vermilingua, (also known as xenarthrans and edentates, it contains anteaters, armadillos and sloths) Spiny anteaters are in the family monotremes (also known as Monotremata and egg-laying mammals, it contains Spiny anteaters and the platypus).

Yes