What is the meaning of the sentence 字了一?
This is a good question.

字了一 should be understood as: 


  (and his) 字 (is) 了一


Thousands years ago, many people in China have a special name besides their first name and last name though nowadays most of Chinese don't have one. And this special name is often described after '字'. For example: 刘备，字玄德.

According to some reference in Chinese, 字 sometimes can be changed. For example, 关羽 was using 长生 as his 字 but then changed to 云长 (which is mostly known by all Chinese)

字 can be given by a person himself/herself or his/her friends, mentors. While ordinary names were mostly given by the parents.