I have Lightroom 4.4.1 running on 2009 MacBook Pro with OS 10.7.5. Every thing works great for my business but my Safari is getting incompatible with certain sites. If I were to upgrade to a current OS 10.13, would my Lightroom 4 e still compatible?
10.13 (High Sierra) is still in beta testing and not expected to be released to the public until the fall. The current version of Mac OS is 10.12 (Sierra) so perhaps you should upgrade to that first. There is no guarantee that older software will be compatible.