Lahmi is mentioned in 1 Chronicles 20:5
And there was again war with the Philistines, and Elhanan the son of Jair struck down Lahmi the brother of Goliath the Gittite, the shaft of whose spear was like a weaver’s beam.
However, other versions translate the verse differently. For example, the NET has
There was another battle with the Philistines in which Elhanan son of Jair the Bethlehemite killed the brother of Goliath the Gittite, whose spear had a shaft as big as the crossbeam of a weaver’s loom.
The associated note suggests that Lahmi is a textual corruption of Bethelehmite. The same incident is recorded in 2 Samuel 21:19 (which contains a different textual corruption so that the word “brother” is omitted in some versions).
It seems that we can be sure that Goliath had a brother who was killed by Elhanan. But whether his name was Lahmi or not is uncertain.
It is likely that Goliath was a descendant of the Rephaites, who were also called the Anakites (Deut 2:11) and the Nephilim (Num 13:33). They were distinguished by their extreme height and an additional finger on each hand and an additional toe on each foot. There was a group of Rephaites/Anakites in Gath:
In still another battle, which took place at Gath, there was a huge man with six fingers on each hand and six toes on each foot—twenty-four in all. He also was descended from Rapha. When he taunted Israel, Jonathan son of Shimea, David’s brother, killed him. These were descendants of Rapha in Gath, and they fell at the hands of David and his men. (1 Chronicles 20:6-8 NIV)
The Anakites were once widespread in Israel (Numbers 13:28,33; Deut 9:1-2) but were largely destroyed by Joshua’s invading army except for a remnant in Gaza, Gath and Ashdod (Joshua 11:21-22). It was from this remnant that Goliath’s family came.
We don’t know whether Goliath had any brothers other than the one killed by Elhanan. However, it would have been unusual for a family to have only two sons.