I don't think original world Ren is Lotus' descendant, cause original world Anna didn't ever hook up with Lotus. From what I've heard original world Ren is just lotus' reincarnation instead of them being blood related.
New world Ren is his great grandson just like how Kasumi/Rea are the great granddaughters of Lisa. Makes sense considering how Lisa and Anna/Lotus were from the same generation