Can I change the thickness of grid lines on a Prism graph?

There is no way to do that directly within Prism, but you can paste the graph to Microsoft PowerPoint (or similar program) and make the change there. Simply copy/paste the graph to an empty PowerPoint slide. Click on the pasted graph (if it isn't already selected) and then choose "Draw...Ungroup". (Note that the Draw menu is usually accessed from a toolbar at the bottom of the PowerPoint window.) Click OK when asked if you want to convert to a PowerPoint (or Microsoft) drawing. Ungrouping results in individual objects that can then be edited. You may wish to regroup the objects when you're finished editing.

When you paste a graph from Prism into PowerPoint, the background color is not pasted. If you want a background color, you'll need to create it within PowerPoint.

You can learn more about making PowerPoint slides from Prism graphs in these step-by-step example articles for Prism 3 and Prism 4.