Lan Wangji and Lan Xichen are very stiff, formal people, even if LXC is the smilier and friendlier of the two. Going solely by book knowledge, I think Lan Xichen only ever calls LWJ "Wangji." While Lan Wangji almost solely calls Lan Xichen "Xiong-zhang" 兄长 (older brother - super formal).
There's also an age/respect thing, between older vs younger siblings.
Example: Wen Qing calling Wen Ning A-Ning, and Jiang Yanli calling Wei Wuxian A-Xian. The other way around, Wen Ning calls Wen Qing "jiejie" (older sister) - which is at least a less formal and more intimate term than xiong-zhang compared to LWJ. Wei Wuxian calls Jiang Yanli shijie (usually refers to an older sister who shares the same master - a.k.a older martial sister, because they are not blood related and are in the same sect).
Take a look at this table if you want more details.
no subject
There's also an age/respect thing, between older vs younger siblings.
Example: Wen Qing calling Wen Ning A-Ning, and Jiang Yanli calling Wei Wuxian A-Xian. The other way around, Wen Ning calls Wen Qing "jiejie" (older sister) - which is at least a less formal and more intimate term than xiong-zhang compared to LWJ. Wei Wuxian calls Jiang Yanli shijie (usually refers to an older sister who shares the same master - a.k.a older martial sister, because they are not blood related and are in the same sect).
Take a look at this table if you want more details.
It's... complicated! I'm sorry. XD