Is it proper to use Sr before a lady name when addressing her in a letter?

No, it is not proper to use "Sr." before a lady's name when addressing her in a letter. "Sr." is an abbreviation for "Senior" and is typically used for men, particularly to distinguish between a father and son with the same name. For women, you would use "Ms." or "Mrs." depending on her marital status, or "Miss" if she is unmarried.