I am not aware of the Lumbee... but a few weeks ago, I had a stint of genetic ancestor testing research on the internet (a dozen or so sites) in the context of African American and Native American bloodlines, both in the USA and in Mexico. Interestingly, mostly the genotypes of 'whites' and 'blacks' in the USA, are relatively quite distinct, ie, there has not been a lot of mixing, contrary to popular opinion. This is has been imputed to longstanding segregation laws/behaviors which discouraged mixed marriages. It is assumed, with present trends, that future genetic research on the same topic will reveal quite different results (near future including today's youth) as popular acceptance of mixed marriages has been rising constantly. Which is why geneticists are in such a rush to get in as much data as possible, as mixed marriages at all levels/geographies and immigration are having a very confusing impact in these genetic studies.
However, in Mexico, bloodlines indicate a more thorough mixing of 'whites' and 'blacks' because mostly because 'being black' although not a 'positive trait' were not consistently prevented discouraged from intermarriage.
On 'black' and 'native' blood lines, a different genetic pattern was obvious. There was an initial mixing, upon initial contacts, but since then, 'mixed marriage' rarity has resulted in 'mixed black/native' marrying other 'black'. Resulting in these 'claims' for 'native status' by certain groups of 'apparently black' Americans. A couple of these claimant groups have 'native' blood ancestry in the vicinity of up to 12%, which is sufficient for the USA government to be declared 'native status', but has no impact on Tribal Council decision making. Tribal councils refuse to incorporate genetic ancestry assessment into their tribal membership laws, they accept only documented descendants of persons specifically listed on certain 1800s lists.
Hope this aids you somewhat in your search, if you haven't done so already, try Googling: genetic native african american ancestry and genetic ancestry testing kits.