"Can Capital Gain income from a Living Trust be distributed to the beneficiaries on the K1s?"

Living trusts (aka revocable living trusts or grantor trusts) are considered disregarded entities for federal income tax purposes and do not issue K-1s. Rather, the income is allocable to the grantor and reported on the grantor's income tax return (typically via a grantor information statement).

See https://www.irs.gov/instructions/i1041#idm140376241113280