They can mean the same thing but not always.
"Lunchtime" refers to the time of day when most people have their lunch.
e.g., Can we meet tomorrow in the plaza around lunchtime? or
I went to a lunchtime concert last week.
"Lunch hour" refers to the hour people take during their work day to have their lunch.
e.g., I was so busy yesterday that I took my lunch hour at 3 pm.
or I'll try to do the shopping during my lunch hour.