Combining :last-child with :not(.class) selector in CSS

Is it possible to choose the last child that does NOT have a class attr? Like such:

<tr> ... </tr>
<tr> ... </tr>
<tr> ... </tr>
<tr class="table_vert_controls"> ... </tr>

I want to select the third row, in this case.

I tried the following, which did not work:

tr:not(.table_vert_controls):last-child

Thanks in advance.