Currently there is some space between the PlotArea and the starting/ending points of the LineSeries in RadHtmlChart.
To changethat behavior, so that it is similar to the one in AreaSeries  the justified property (https://docs.telerik.com/kendo-ui/api/javascript/dataviz/ui/chart/configuration/categoryaxis.justified) can be set through the underlying Kendo Chart widget:

        <telerik:RadCodeBlock ID="RadCodeBlock1" runat="server">
            <script>
                function onLoad(sender) {
                    var chart = sender.get_kendoWidget();
                    var opts = chart.options;
                    opts.categoryAxis.justified = true;
                    chart.setOptions(opts);
                    chart.redraw();
                }
            </script>
        </telerik:RadCodeBlock>
        <telerik:RadHtmlChart runat="server" ID="LineChart" Width="800" Height="500" Transitions="true">
            <ClientEvents OnLoad="onLoad" />
            <PlotArea>
                <Series>
                    <telerik:LineSeries Name="Week 15" MissingValues="Interpolate">
                        <SeriesItems>
                            <telerik:CategorySeriesItem Y="15" />
                            <telerik:CategorySeriesItem Y="23" />
                            <telerik:CategorySeriesItem />
                            <telerik:CategorySeriesItem Y="71" />
                            <telerik:CategorySeriesItem Y="93" />
                            <telerik:CategorySeriesItem Y="43" />
                            <telerik:CategorySeriesItem Y="23" />
                        </SeriesItems>
                    </telerik:LineSeries>
                </Series>
            </PlotArea>
        </telerik:RadHtmlChart>