The Desired State Configuration (DSC) module xWebAdministration does not yet support changing the identity of an application pool. There is a community fork cWebAdministration that seems to support it – but I have not tested it yet.
What I did was to use the script resource to change the identity using the module WebAdministration. This is pretty straight forward so I just share the code here. Note that after changing the identity the state of the application pool is stopped. You can use the xWebAppPool resource to start it again.
Configuration WebServerConfiguration
{
Node $AllNodes.NodeName
{
Script ChangeAppPoolIdentity
{
GetScript = { return @{ AppPoolName = "$($using:Node.WebAppPoolName)" }}
TestScript =
{
import-module webadministration -verbose:$false
$pool = get-item("IIS:\AppPools\$($using:Node.WebAppPoolName)")
return $pool.processModel.userName -eq $using:AppPoolUserName
}
SetScript =
{
import-module webadministration -verbose:$false
$pool = get-item("IIS:\AppPools\LSK.Services");
$pool.processModel.userName = [String]($using:AppPoolUserName)
$pool.processModel.password = [String]($using:AppPoolPassword)
$pool.processModel.identityType = [String]("SpecificUser");
$pool | Set-Item
}
DependsOn = "[xWebsite]WebSite"
}
xWebAppPool NewWebAppPool
{
Name = $Node.WebAppPoolName
Ensure = "Present"
State = "Started"
DependsOn = "[Script]ChangeAppPoolIdentity"
}
}
}
writeabout.net 
Can you sure with me an example of how this is called in the DSC script? I am pretty new to DSC. I have all sites and appPools creating I am just not how to implement this.