So what your question is tackling deals with American Indian recognition and the United States' federal Indian policy, a very messy subject. Let's get into it.

Within the United States, there are currently 567 federally recognized Tribes. This means that the federal government recognizes 567 groups as being American Indians/Alaska Natives, having inherent sovereignty as said people, and having a trust relationship with the United States predicated on treaty relations. According to the Federal Register, the Lumbee Tribe is not listed as being recognized and to receive services from the federal government. However, they do have recognition as part of the Lumbee Act if 1956. There is a reason for this.

In 1871, the United States formally ended the treaty making process with Tribes, but stated that all treaties previously made would remain in affect unless they are properly abrogated by Congress. From this point onward, the United States had an evolving relationships with Tribes.

In 1887, the General Allotment Act, also known as the Dawes Act, was passed. This act was Congressional legislation that, because Tribes were being moved onto reservations, Congress thought they could pass because they were gaining "oversight" of American Indian Tribes. In 1924, all American Indians were granted U.S. citizenship if they had not received it under the General Allotment Act. In 1934, the Indian Reorganization Act was passed, which restructured Tribal governments in a way that the United States saw fit. However, by 1953, the federal government had decided they no longer wanted to uphold their treaty obligations and the trust responsibility to Tribes. Instead, because they declared themselves as having "plenary," or absolute, power over Tribes and because they had essentially taken "oversight" of them, they could terminate the recognition of these Tribes. Mind you, this had all occurred through Western standards of thought and jurisprudence and since Tribes were being subjugated for much of this time, they couldn't necessarily resist to a full measure the desires of the United States by the late 19th Century, let alone the middle of the 20th Century.

By 1953, the federal Indian policy of the federal government entered what is known as the "Termination Era," a time in which 109 Tribes had their federal recognition terminated and services provided by the Department of the Interior and Bureau of Indian Affairs, as well as whole reservations, were suspended and dissolved, stripping the protections in the treaties down to their bare minimums and practically erasing those Tribes as polities. In the case of the Lumbee, who were fighting for federal recognition during the 50s, they won their struggle...in 1956. Scholar David E. Wilkins, who is of Lumbee ancestry himself, writes the following:

After the Lumbees were acknowledged by North Carolina, they then launched their drive for federal recognition. Three years later, on June 7, 1956, Congress passed "An Act Relating to the Lumbee Indians of North Carolina."(83) The federal law used language nearly identical to that of the state law. However, at the request of the Department of Interior-the agency spearheading the national termination policy-an exclusionary clause was inserted providing that "nothing in this Act shall make such Indians eligible for any services performed by the United States for Indians because of their status as Indians, and none of the statutes of the United States which affect Indians because of their status as Indians shall be applicable t[o] the Lumbee Indians."(84)

Ironically, then, the 1956 federal law acknowledged the Lumbees as a distinctive tribe, yet simultaneously precluded them from the federal services and protection generally provided to other acknowledged tribes. In other words, the tribe was recognized and terminated in the same legislation (McCulloch & Wilkins, 1995).

Therefore, because the federal government assumes "plenary power" over Tribes and sees their legislation as being applicable to establish sovereign entities, namely the Tribes, they saw the passing of termination legislation as "legal" and being within their power, something which the Supreme Court also supported. Since the Lumbee just happened to win their recognition during the time of Termination, Congress eliminated the provision for treaty protected services from the bill they passed to recognize the Lumbee. That is why they are acknowledged as being Indians, but do not receive any federal services.

References

McCulloch, A. M., & Wilkins, D. E. (1995). "Constructing" nations within states: the quest for federal recognition by the Catawba and Lumbee tribes. American Indian Quarterly, 19(3), 361-388.