Lords of the Fallen healing upgrades and Sanguinarix guide

How do you upgrade the Lords of the Fallen Sanguinarix? Put simply, the Sanguinarix is this soulslike game's equivalent of an Estus flask. It provides quick healing that can be recharged at any bonfire-like checkpoint, but once you run out, you're often not left with many options for long-term survival.
Our Lords of the Fallen review does state that the game wears its influences on its sleeve, with the Lords of the Fallen Sanguinarix being such a case. While there are also Briorstones in Lords of the Fallen that you can use to heal in a pinch, as well as really handy pieces of jewelry you can equip, the main way you heal is by using the Lords of the Fallen Sanguinarix. So here is what you need to do to upgrade it and maybe last long enough against the Lords of the Fallen bosses to make it to the Lords of the Fallen beacons in order to cleanse them.
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