It is two words.
"Homecooked" is typically written as one word.
"Lifetime" is one word.
mobile home
In internet usage, homepage is one word.
hometown is usually one word
"Homebuilder" is typically written as one word.
"Homework" is typically written as one word.
one
Mobile home, two words.
Lifestyle, life style, or life-style. All can be used.
"Home sale" is typically written as two separate words.
There are 2 syllables in the word "homemade":home/made