How can I draw an arrow without using a line?

Hi Steven thanks for posting in the Lucidchart Community! 

You can achieve this by drawing an arrow from the circle switching the line options of this arrow to curved and then adjusting the curvature of the arrow to fit your circle. Alternatively you can open your page settings and disable "Snap to Grid" and "Line Connections". This will prevent your line from snapping onto the grid or to objects which will in turn allow you to freely arrange the arrow on your circle. Once you have arranged the arrow I would recommend selecting both the arrow and the circle and grouping them (right click > Group).

I have recorded GIFs showing both of these options:

For more information on lines in Lucidchart please take a look at the Add and style lines in Lucidchart article in our Help Center. Hope this helps!