Lakorn is just the Thai word for a drama series. So any series from Thailand is a lakorn. Like you say K-drama when you talk about a drama from Korea, you say lakorn when you talk about a drama from Thailand.
"The Series" is often added to titles of lakorn that are published on the internet instead of on television. I think in the beginning it was added to English titles that were rather short and often associated with other things. For example if your lakorn would be called "I love you" and you type that into Google you are not gonna get the lakorn as your first search result. But if you call it "I love you The Series" then the drama is probably the first entry you get. Then it became somehow the norm for web lakorn to have "The Series" in the title even if the normal title is a rather unusual phrase.
Also the stories are often based off of web novels or just normal novels so the title is already the search term for the novel. When you add "The Series" at the end you make it clear that you are refering to the lakorn.
I hope that answered your question... ^^
