I'm hoping the answer to this is yes, as in illustrator I found a cool trick to make lightning effects by varying the width of paths

https://www.deviantart.com/torkuda/art/They-Meet-833448114

Anyone know how to do this in inkscape? Basically, say I want a normal width path and want to narrow the path only in the middle, how might I do that?

If it's a path, you can use Path > Dynamic Offset

Which should allow you to change the size of objects to make something thinner.

It's not stroke, it's fill in this case. But it acts much like a line.

In addition to Dynamic Offset mentioned by Martin, you could use Stroke to Path, from the Path menu. A black stroke will now have a black fill with a stroke around it (if that makes sense) and that can be pulled and stretched varying its thickness, like the example you included.

There is a relatively easy way to do that with Path > Path Effects ... (Ctrl-&) and then select Power Stroke. You will then get a pink node somewhere along the path, which allows you to change the width. To make it variable, add another node by Control-Clicking the pink node (it doesn't work elsewhere for me). There is a page on the wiki about it it seems [1]. I'm using  Inkscape 1.1.

[1] https://wiki.inkscape.org/wiki/index.php/PowerStroke

And there is the "Shape:"-property of the drawing tools.

See also PowerStroke LPE for further effects/features.