An upper-secondary school is a senior high school. Then is a lower-secondary school a junior high school? Where is the expression 'a lower-secondary school' used?

I believe that is used in the United Kingdom.

We also have middle schools which are similar to junior high schools.

Yes, you are correct. A lower-secondary school is typically equivalent to a junior high school. It is a school that is attended by students in the age range of approximately 11 to 14 years old, typically covering grades 6 to 8 or 7 to 9, depending on the education system of a particular country.

The term "lower-secondary school" is commonly used in some countries or regions to describe this educational level. However, it is important to note that the specific terminology and organization of schools can vary between different countries and education systems. Some places may use the term "middle school" instead of "lower-secondary school" to describe the same educational level.

To find out where the expression "a lower-secondary school" is used, you can refer to the educational systems of specific countries or regions. Different countries have different terms and definitions for their educational levels, so it's essential to consider the context in which the term is used.