The “lower church” mentioned in the way you describe is generally a worship space or chapel in the basement area or lower level of a church building. Often it’s smaller and less ornate, and is often used for stuff like daily Masses or vespers.
The “upper church” would generally be the large main church space that is typically used for Sunday Mass and other large gatherings.
It is also possible to have two Masses going on simultaneously with one in the upper space and one in the lower space, if there’s a demand for Masses. For example, you might have the English language Mass in the upper church and the Polish language Mass in the lower church at the same time.
Many older pre-1950s churches have an upper and lower church.
This has nothing to do with “high church” and “low church” in Anglican usage.