That’s right, and as always it’s interesting to do some digging. I should mention that I consider the following general order for the age of the Nikayas: SN, AN, MN, DN
E.g. in SN 12.66 we find
Bhikkhus, whatever ascetics and brahmins in the past regarded that in the world with a pleasant and agreeable nature as impermanent, as suffering, as nonself, as a disease, as fearful: they abandoned craving.
Here we have the lakkhana in the context of some asubha-practice. And also we have five of them, not three.
Then we have more detailed list, again of basically asubha saññā practices like “Anicce dukkhasaññā”, “Dukkhe anattasaññā”, “Pahānasaññā” in SN 46.67-76.
Which is repeated in a way in SN 55.3:
dwell contemplating impermanence in all formations, perceiving suffering in what is impermanent, perceiving nonself in what is suffering, perceiving abandonment, perceiving fading away, perceiving cessation.
So the SN at least doesn’t have three lakkhana at all afaics. It continues with AN 1.465-474, again ten perceptions, not three. And as before AN 4.49 puts them in an asubha context:
Perceiving permanence in the impermanent, perceiving pleasure in what is suffering,
perceiving a self in what is non-self, and perceiving attractiveness in what is unattractive,
beings resort to wrong views, their minds deranged, their perception twisted.
AN 5.72, AN 5.305 has (no surprise) five perceptions:
The perception of impermanence, the perception of suffering in the impermanent, the perception of non-self in what is suffering, the perception of abandoning, the perception of dispassion.
AN 6.35, AN 6.142 add nirodha. AN 7.58 has these seven items:
The perception of unattractiveness, the perception of death, the perception of the repulsiveness of food, the perception of nondelight in the entire world, the perception of impermanence, the perception of suffering in the impermanent, and the perception of non-self in what is suffering.
Etc. etc. you see where this is going, the lakkhanas appear in the context of specific advanced asubha, or more generally dispassion practice. As so often we don’t find an ontological, philosophical description of “existence” but a pragmatic approach to overcome any clinging to whatever appears to be desirable or attractive.