Liz Buchanan BVSc MRCVS
Keymaster
Hello!  I'm afraid I'm not sure. Two possibilities jumped out:
1) A crust of pus, oozing from the skin, that could be sticky or could flick off under your finger, with a wound or damaged skin underneath.  If so, it could be due to superficial bacterial dermatitis or contact with something skin-damaging or some irritant. These tend to be sore and develop / worsen quickly.
2) The remains of something that has otherwise been eaten by your cat - and if that's the case, and the animals are all lethargic, I would might be concerned that toxin ingestion may be a strong possibility, until proven otherwise.
3) Certain infectious diseases.
However, just to be clear, the mouth crusting could in theory be independent of the lethargy. Either way, contacting the emergency vet to be triaged (i.e. for them to decide whether to see you right now) would be a very good idea. Best of luck - and please let me know what is found.
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