The Truths would always be different to each individual. Do you mean if there's a pattern to the kind of Truth one speaks within the sequence? We don't know. Perhaps there is a pattern there, with certain kinds of Truth or how powerful the Truths were. In simpler terms, whether admitting to a certain kind of falsehood per stage or how powerful the lie was in the speaker's life, etc. Perhaps we'll know when Shallan's Squires Gaz, Vathah, Red or Ishnah swear their own Truths
Your idea isn't wholly off the mark either. Lightweavers don't bind themselves to any moral codes except to their own conscience. They're about self-awareness, self-actualization and self acceptance, admitting the lies one tells themselves, accepting harsh truths about oneself, being honest to oneself. Not necessarily easier than following Oaths but certainly... free-er, in a sense.
So some people can certainly wonder if Lightweavers are one of the more potentially easier to go bad, the more corruptible among the Orders. But I don't believe so, since the process of becoming a Lightweaver would make one more honest to themselves, they'd admit their faults. The other Orders on the other hand could go "for the greater good" or put their own conscience and sense of morality above what might need to be done.