I am not sure whether patient needs to be plural or singular in the title sentence. If it's plural is it then "patients' lives"?
- "This positively affects patient lives and"
- "This positively affects patients' lives and"
In the first sentence, the group "patient lives" is a compound noun. Here you should just pluralize the last noun of that group.
In the second sentence, the group "patients' lives" is a genitive construction. Here you should pluralize both nouns.
Both sentences are valid and their meaning is equal.