If you’re referring to the “latest” list on the categories page, then this is what you need to change:
If you want the avatar of the topic creator, you need to pass that instead, so you go from
{{#user-link user=topic.lastPoster}}
{{avatar topic.lastPoster imageSize="large"}}
{{/user-link}}
to
{{#user-link user=topic.creator}}
{{avatar topic.creator imageSize="large"}}
{{/user-link}}
So something like this in the header section of your theme
<script type="text/x-handlebars" data-template-name="components/latest-topic-list-item">
<div class='topic-poster'>
{{#user-link user=topic.creator}}
{{avatar topic.creator imageSize="large"}}
{{/user-link}}
</div>
<div class='main-link'>
<div class='top-row'>
{{raw "topic-status" topic=topic}}
{{topic-link topic}}
{{#if topic.featured_link}}
{{topic-featured-link topic}}
{{/if}}
{{topic-post-badges newPosts=topic.totalUnread unseen=topic.unseen url=topic.lastUnreadUrl}}
</div>
<div class='bottom-row'>
{{category-link topic.category}}
{{discourse-tags topic mode="list"}}
</div>
</div>
<div class='topic-stats'>
{{raw "list/posts-count-column" topic=topic tagName="div"}}
<div class="topic-last-activity">
<a href="{{topic.lastPostUrl}}" title="{{topic.bumpedAtTitle}}">{{format-date topic.bumpedAt format="tiny" noTitle="true"}}</a>
</div>
</div>
</script>
there’s more on template overrides here