Thread safety ??

This doubt is regarding synchronisation question in Singleton pattern code
of C#

I had created a class as

public sealed class SecuriteManager
{
private static volatile SecurityManager instance;
private static object syncRoot = new Object();

private SecurityManager () { }

public static SecurityManager GetInstance
{
get{
if(null == instance){
lock(syncRoot){
if (instance == null)
instance = new SecurityManager ();
}
}
return instance;
}
}

public bool IsAllowed(strin g UserName)
{
//A very long process here.
//For example access to a webservice which might take 3 seconds.
//HttpContext.Cur rent.Session[UserName] = returnValueFrom Webservice;
}
}
Now when 2 users access IsAllowed at the same time, is the process thread
safe ?
Or should I use lock for each call in my function as

public bool IsAllowed(strin g UserName)
{
lock(syncRoot)
{
//A very long process here.
//For example access to a webservice which might take 3 seconds.
//HttpContext.Cur rent.Session[UserName] = returnValueFrom Webservice;
}
}

Please suggest.