Maybe. Depends! Patients often feel their heart beats more at night, not because something happens to them when they lie down (though bad dreams and aggravation can cause palpitations!). It's usually a "signal to noise" issue, i.e., lying down in a dark, quiet room may "unmask" underlying awareness of heart beat because there's less external stimuli to interfere. Talk to your doctor to check 24° rhythm.
Yes. I see this often in patients, its unclear what is going on, but i think it may sometimes be related to the fact that when one lays down, more blood flow reaches the heart from the feet and causes the heart palpitations. A solution may be to first raise legs in a chair for 15 minutes then lay flat. Would be curious to know if this helps. Of course, one should rule out heart disease or svt ct.