If you're laying down and it becomes harder to breath, is that asthma?

Maybe... There are many entities that cause one to be short of breath when lying flat. Asthma is one but others include diaphragm dysfunction, congestive heart failure, etc. Thus, you would need to have this symptom evaluated by your doctor so the correct diagnosis and treatment could be initiated.
Not necessarily. Orthopnea, or trouble breathing lying down, is common with certain heart conditions.