What was lady Jane grey job?

If you mean did she work for a living then the answer is no

Few if any women in 16th century Britain had any kind of "job" other than wives and mothers.

Lady Jane Grey was an English Noblewomen executed after only 9 days on the throne of England at the age of only 16 or 17.

It was noted that Jane acted as chief mourner at Catherine Parr's funeral