Hello and hope you are doing well.
The other causes for night time cough besides asthma are GERD and post nasal drip from allergies. GERD is gastro esophageal reflux disease where the stomach acids come back into the esophagus and spill into the wind pipe causing cough. Treatment with antacids will help neutralize the acids. Post nasal drips can occur with sinusitis and throat infections. Giving up cigarettes will abolish smoker's cough in 90% of people. Talk to your GP about the other causes for cough in the meantime he could try warm salt water gargles and breathing exercises.
Hope this helped and do keep us posted.
There are many possibilities here...
He may have developed pneumonia from laying around too much ( this tends to happen in the elderly who already have weakened immune systems).
He may have postnasal drip ( PND) which causes you to cough because it is dripping down your throat...and is worse at night when laying down.
You could try propping him up on pillows or raising the head of the bed, which helps quite a bit for PND. Using a humidifier will help as well.
There are other possibilities, but only a trip to the doctor will help in determining what the cause is.