I have seen that bio pic and it was a good one.
However, please try to get the facts straight. Lilly was never married to Edward VII. His only wife was Alexandra of Denmark. Edward had many many mistresses and Lilly was one of them.
If you just read around the forum or do a search, you will find a lot of information on Edward VII, Lilly Langtree and Louis Mountbatton (Louis of Battenberg). Louis was married to Victoria of Hesse who was Alix of Hesse's sister (Alexandra of Russia).
And as was already pointed out, Louis always admitted to being the baby's father and never pretended that he wasn't. This affaire took place before Victoria and Louis were married.