In some cases, according to a condition, after the data from a request arrives, the developer may want to prevent further requests from this same tile. This should be possible by setting the update interval to 0.

In the meantime, you can add dynamically (and remove when needed) a handler for the OnClientDataLoading event that will cancel the event and thus - the request. For example:
			<telerik:RadLiveTile ID="MyLivetile" UpdateInterval="1000" OnClientTemplateDataBound="MyLivetile_OnClientTemplateDataBound"
								 runat="server">
				<WebServiceSettings Path="Default.aspx" Method="MyPagemethod" UseHttpGet="false" />
				<ClientTemplate>
					some template that uses the data
				</ClientTemplate>
			</telerik:RadLiveTile>
			<script type="text/javascript">
				function MyLivetile_OnClientTemplateDataBound(sender, args) {
					var completed = args.get_dataItem().Completion;
					if (completed) {
						sender.add_dataLoading(preventLiveTileRequests);
					}
				}
				
				function preventLiveTileRequests(sender, args) {
					args.set_cancel(true);
				}
			</script>