Both are ok.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Vincent TeoThey saw / watched a live parade on the television.Not idiomatic. It implies they could also watch a dead parade, which is rather bizarre I think.
Vincent TeoThey watched a (national ) parade live on TV.Fine. The grouping is not [parade live]. It's [live on TV], which means that you are watching the event as