Lines is not the answer I wanted to hear. The concept of lines is particularly problematic as Word has no fixed way of handling it.
For instance, how many lines in a table containing multiple columns? How many lines in a graphic? Do we count empty paragraphs, hard page breaks, section breaks etc.?

One feature you might want to consider is turning on Layout > Line Numbers. This will show you that tables are excluded from the numbering.
On any given page this should return the line number on the page - unfortunately it returns odd results when tables appear before it. It seems to include some but not all cells.
Selection.Range.Information(wdFirstCharacterLineNu mber)

As far as I can tell, you would then need to iterate through all preceding pages to work out how many lines on each page and add them all together.

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Andrew Lockton
Chrysalis Design, Melbourne Australia