Is $L_p$ decidable when p is a trivial property?
If $p$ is a trivial property of r.e. languages, it either applies to all r.e. languages or applies to no r.e. language. That means that either


$L_p$ is the set of all TM descriptions or
$L_p=\emptyset$.


In the first case, a decider for $L_p$ ignore the input $\langle M\rangle$ and immediately accept and in the second case, a decider would similarly reject. In either case, $L_p$ is clearly decidable. While we don't necessarily know which decider is the right one to use, that doesn't matter, since the existence of a decider is all that we need.