The file "http://servername/sites/Testing/test123/test.docx" is checked out or locked for editing by SHAREPOINT\system

Whenever you are trying to update the properies of an Item in ItemAdded Event of a Document Library. Need to use base.DisableEventFiring/base.EnableEventFiring before and after an item added. Refer the below sample source code for your further use,

Code Snippet:

public override void ItemAdded(SPItemEventProperties properties)
{
base.ItemAdded(properties);
try
{
base.DisableEventFiring();
SPListItem oItem = properites.ListItem;
oItem["ItemName"] = "Testing";
oItem.SystemUpdate(false);
}
catch(Exception err)
{
Console.Write(err.Message);
}
finally
{
base.EnableEventFiring();
}
}