Or HaChaim on Genesis 13:8/אור החיים על בראשית י״ג:ח׳

1 אל נא תהי מריבה, Let no quarrel develop between me and you. Abraham told Lot that what had started as an argument between their respective shepherds was bound to lead to a quarrel between the two of them even though Lot claimed that he would never allow this to happen. After all, he respected his uncle too highly as the senior member of the family. The substance of the shepherds' arguments concerned the fact that Lot allowed his shepherds to graze on privately owned land, counting on G'd's promise that the land would belong to Abraham's family in the future. Seeing that Abraham had no children and was genetically unable to father children, Lot viewed himself as Abraham's heir. Abraham alluded to this by the superfluous comment that they were brothers.

2Another reason Abraham referred to their being brothers may be understood in light of our sages' comment on Psalms 50,20 [I have not found that commentary. Ed.]. The Psalmist describes a brother who lives with another brother as maligning him. Applied to our context this means that Abraham was afraid that if the local inhabitants would take Lot to court for stealing from them, his own reputation as the elder brother (uncle) would become tarnished. He could not allow this to happen.

3Abraham may also have hinted to Lot that the very fact that their principals were brothers made Lot's shepherds take that relationship for granted. Familiarity breeds contempt; had the two not been related, Lot's shepherds would have given Abraham the respect due him as an elder and as a person whom G'd had obviously favoured.