As @ROSt53 has indicated it is not possible to currently create in-line / run-in lists using list styles or list-related direct formatting options. Generally this type of list is ordered (each item uses an alphanumeric identifier) rather than unordered (where each item uses a bullet or shape identifier). There is no workaround that I am aware of.
List styles can only be associated with paragraph styles and what is essentially being requested is to associate a list style with a character style. Exactly how this would work using direct formatting (existing toolbar buttons or the Format > Bullets and Numbering… menu) is unclear. ODF v1.2, 5.3.4 states:
The <text:list-item> element has the
following child elements: <text:h>
5.1.2, <text:list> 5.3.1, <text:number> 6.1.10, <text:p>
5.1.3 and <text:soft-page-break> 5.6.
In simple terms, a list item can be a heading, sub-list, or paragraph, and the form of a list item in the XML is generally a paragraph, whether using direct formatting:
<text:list-item>
<text:p text:style-name="P2">Item 1</text:p>
</text:list-item>
… or a list style associated with a paragraph style:
<text:list-item>
<text:p text:style-name="List_20_1">Item 1</text:p>
</text:list-item>
Instead, what is likely required, is some sort of use of the <text:span> (i.e., character style) element, e.g.,
<text:list-item>
<text:span text:style-name="List_20_1">Item 1</text:span>
</text:list-item>
Enhancement request fdo#82433 appears to have been raised as a result of this question.