I have a diagram where text intersects with lines. I'd like to break the line so that it does not overlap with the text, preferably avoiding having to draw a white rectangle between both.

What would be the best way to achieve that?

Here are three methods.

1.  Add nodes and break the line. (I mostly use this.)
2. Clone LPE and increased stroke width.
3. Bounding Box LPE and Offset LPE.

Quick and repeatible way for solution 1.

Enable snapping to bounding boxe's edges and cusp or smooth nodes. Use node tool to select line, double click when it snaps to bounding boxes edges. Then hold ctrl key and double click on segment to delete.

BTW solution n°3 is a brilliant one. Sadly, seems buggy if you add an inverse clip to line. Maybe a mask ? 

Thanks! Indeed I think I was making things too complicated, and the first method is the easiest. It looks like more manual work, but in the end, it's less operations.