For me, this loops over the IPs fine. There is an easier way to do in PowerShell though using foreach.
And remove Format-Table; it is useful when writing to host but just turned your nslookup result to Microsoft.PowerShell.Commands.Internal.Format.FormatEntryData datatype.
Use -Append with Out-File to avoid overwriting previous result.
$ipAddress = @('107.20.253.26', '107.20.178.220', '8.8.8.8')
foreach($ip in $ipAddress) {
# remove Format-Table
$resolve = nslookup $ip
# Add Append flag so that you are not overwriting previous contents on each loop
$resolve | Out-File $resolveFile -Append
}