Your options are either upgrading to Lightroom 6.13 (perpetual) or to subscribe to Lr Classic CC (current version is 7.01, Photoshop comes with the subscription) or Lr CC (cloud based, 1TB of cloud image space.
Before you upgrade your MacOS: Do a complete backup of your system.
After the upgrade: try Lr on your Mac and if all goes smooth, buy either Lr 6 or the subscription.
With Lr 6 you need to know that it will be phased out at the end of the year with a last update. It is the last perpetual license of Lr you can buy. If you want to evolve (well I suppose you do not have the urgent need to evolve anyhow), you need to buy the subscription of Lr Classic CC for around 12€/month (including Photoshop) or to buy the subscription of Lr CC with 1Tb of cloud space.