Is this HTML structure valid? UL > DIV > { LI, LI } , DIV > { LI, LI } , DIV > { LI, LI }

No, div is not allowed as a direct child of ul. Whenever you’re in doubt, validate your page with W3C or check the corresponding article on W3C:

4.5.6 The ul element

Categories
Flow content.

Contexts in which this element can be used:
Where flow content is expected.

Content model:
Zero or more li elements.

Content attributes:
Global attributes

DOM interface:
interface HTMLUListElement : HTMLElement {};

Instead you could use

<ul class="blog-category">
    <li class="three column">
        <ul>
            <li>Item 1</li>
            <li>Item 2</li>
            <li>Item 3</li>
        </ul>
    </li>
    <li class="three column">
        <ul>
            <li>Item 4</li>
            ...
        </ul>
    </li>
</ul>