There are 8 possible combinations in this puzzle: 2 states of being (knight or knave) amongst 3 people. 2 ^ 3 = 8.

With no other intuition, we could plug in scenarios and check the statements which wouldn't take too long but one statement is more easy to verify than the others.

Start with Lil, who claims that Ben and Ted are not knights. We'll change the wording but keep the logic: Ben and Ted are knaves. In this scenario, Lil is a knight.

Assuming Lil is a knight, her statement about Ben and Ted is true. Knights never lie.

Now we can take their statements and see if they are lies which would confirm their status as knaves.

Ted said "at least one of the following is true, that Lil is a knave or that I am a knight."

We're operating on the assumption that Ted is a knave, which holds true because both parts of his statement are false: he is not a knight and Lil is not a knave.

So far so good.

Ben said "Ted could claim that I am a knave". Again, we're thinking Ben IS a knave, in which case he is ALSO lying. Ted, a knave, could not accurately identify Ben as a knave.