"lesser position" is correct and usable in written English.
You can use it to refer to a lower rank or level of something, such as a job title or authority. For example, "He got promoted to a higher position after holding his lesser position for several years."
If you lose, would you accept a lesser position?
Instead, the lesser position of National Secretary is to be created.
Tower Club president Rachel Macaulay '19 said she considered seeking a lesser position, but decided that she would rather handle the big-picture issues facing the club.
History, even more enlightened recent history, is not overendowed with men who are comfortable with taking a lesser position in the spotlight.
Indeed that "David" shirt is a brave attempt by Dolce & Gabbana to paper over the crack that keeps men's fashion in its lesser position.
From a lesser position in the government or the party, Mr Ozawa might conceivably wield greater clout than the gentle Mr Okada.
Yet none of the incumbents were fired, only moved to arguably lesser positions.
Then they will learn if their jobs remain open, if they have been reassigned to other, lesser positions, if they have permanently poisoned relations with their bosses.
It looks like the Senate will be spending a lot of time failing to pass Obama nominees for federal judgeships, cabinet posts and lesser positions.
He held a number of lesser positions before becoming professor of divinity at the Universities of Durham (1940 50) and Cambridge (1950 52), bishop of Durham (1952 56), and archbishop of York (1956 61).
He should fill not only his cabinet but the many lesser positions with professionals from outside the circle of elite names and regional political families — and be merciless if they misbehave.
