I am a student who lodge in the school

没错啊。你是不明白什么？

翻了翻资料，有个句子是这样的：
Many students lodge in their college halls.

所以，照你的句子看lodge及整个句子的用法没有错，只是如果可以的话就不要用school吧！school指的毕竟是学校，而你要表达的大概也是宿舍吧。

I am a student who is lodging in the school.
or: I am a student who is boarding in the school.

小建议楼上:I'm a student in a board school.

应该对，就是这个lodge有待商议

lodge改为lodges

我是一个在学校里被投诉的学生