OK, so brother of the Lord could be a title reserved for James because of his position within the church which is what has been suggested by R. M. Price and others. I see.
You have to laugh at the sheer audacity (idiocy?) of the illogical argument the mythicists put forward here. And I find it suprising that you, who are so keen to accuse others of simply building all their arguments on baseless assumptions, don't have a problem with it.
First, Price "leapfrogs" over the evidence in Josephus (not to mention ignores the independent attestation in the synoptic tradition). Then, the argument runs as follows, ending with a conclusion achieved solely by assuming it to begin with:
1) Jesus was a myth, therefore he couldn't have a brother
2) Paul calls James the brother of the lord, the title he refers to Jesus by.
3) Paul can't mean a literal brother.
4) Therefore, "brother of the lord" must be a title of some sort that DOESN'T mean a literal brother
Conclusion: The mythicist hypothesis is not disproven or problematic in anyway because of Paul's reference to Jesus' brother.
That's great, only you get to the conclusion by assuming it in the first place. There is no evidence for Price's speculation that this is some title. Nor does Price offer an analysis of the greek that would explain why we see a typical kin identification construction. Another explanation is offered without any basis, nor any argument put forth as to why the best and typical rendering is wrong, other than it can't be right given an assumption of a mythical Jesus.
Again: If you want to argue that the construction Paul uses is NOT a means to identify James by his brother, then 1) what is the genitive doing here and 2) how can you show this by other examples in Greek?