英语教师正在上课可以用 "The Engpsh teacher is giving a lesson." 来表达。

例句：

The Engpsh teacher is giving a lesson right now.
The students are paying attention to the Engpsh teacher's lesson.

你还可以用其他表达方式来描述，例如：

The Engpsh teacher is teaching a class.
The Engpsh teacher is depvering a lecture.
The Engpsh teacher is conducting a lesson.