JLA Adventures is set in the "present day" but it's ambiguous as to when exactly that is.
It's stated: "This is Lex Luthor. It says here his body was found in the year twenty-eight fifty-six." Lex Luthor then states "The year twenty-eight fifty-six. I've been frozen for nearly a thousand years." This can't be true due to simple math. If 2856 minus 1000 equals 1856, then that would place the opening "present day" scenes in 1856, which doesn't line up with the technology being shown.
However, Lex does say "nearly a thousand years". This is vague enough to make it 881 years or so instead of 1000. 2856 minus 881 equals 1975. Lex Luthor then states: "I am Lex Luthor, and I want you to take me back in time. A thousand years ago, to be exact." If he is travelling from the 31st century, this would take him to the early 2000s..
After time travelling, the two Legion Of Superheroes members ask_"Are we truly a thousand years in the past? Looks like it."_ Due to the technology, it can't be 1856. Dawnstar then states "Remember this is the twenty first century, a time of great ruthlessness." Since 1856 took place in the 19th century and the characters believe they are in the 21st century, the most logical conclusion is that there is a continuity error and the characters mistakenly believe they are in the 21st century, when in fact they are in the 20th century.
Later, it's stated: "I am Dawnstar. This is Val Armorr, also known as karate Kid. We're from the future. The thirty first century. A thousand years from now. The one you know as Lex Luthor had been discovered in the year 2856 during the big thaw of the second warming. It took a massive ice thaw and hundreds of years for civilization to find Lex frozen in this wasteland." The 31st century spans the years 3001 - 3100. It makes more sense that this film is set in the 1970s.
This film takes heavy inspiration from the "Super Friends" franchise which began airing in 1973. Batman and Superman's designs resemble their Earth Two comic counterparts of the 1970s.
