Thanks for placing your query through HCM.
I can appreciate your concerns.
The by seems to be going through a tough time.
Lips turning blue could be due to dehydration
or is he very cold
or even the cough
Being very sleepy, fatigued & poor intake are worrisome enough to take him to Emergency dept.
In the meantime continue giving him small sips of fluids & make sure he is not cold.
Hope I have answered your query.
Take care of him.
wish him good health.