I like the factor that it can dispel illusions (burning away falseness) and Perez occasionally used it as a way to protect others in a purifying or purity sense. In the early beginnings of the Circe tale I recall Diana using the lasso to create a protective ring on the ground that protected Nessie from the marauding Beastiamorphs by the blazing fires of Hestia.
I quite like those two powers, along with the truth-telling abilities. Add in that it can only be untied by a god and I'm happy with that short list of the lasso abilities. (That's powerful enough for me, given all of Diana's other awesome abilities and strengths.)
As for believing one's own lies, that's a bit of a conundrum. I lean toward they ensnared tells it like they see it to Diana or through the bond in the lasso Diana sees a shrouded "layer of truth" that the subject has so deeply subverted that Diana can only see it's there, but not necessarily understand what it is.
Or, if the lasso's power is absolute, any deeply hidden truths come down to a battle between the wills of Diana and the "lassoed." With his tele-powers, I kind of see it going down this way between Diana and Doctor Psycho...who I'd estimate might be one of the strongest and most ferocious opponents of the fires of Hestia. (With good reason too.)