This statement does return TRUE, and will do so no matter what you enter. If you enter A, it results in TRUE because A is not equal to PTR. If you enter PTR it results in TRUE because it's not equal to A. Anything else is not equal to both of them.
The problem here is that you want it eventually return FALSE, so you can move past the while loop to the next section of code. To do this, you need a -and instead of a -or.
$lookupDecision = Read-Host "Do you want results for A or PTR: "
while( $lookupDecision -ne "A" -and $lookupDecision -ne "PTR" ) {
$lookupDecision = Read-Host "Invalid input! Enter A or PTR: "
}