A strap will let you secure the dulcimer even if you lap is not perfectly flat. It will also, if you wish, allow you to angle the dulcimer slightly up, lifting the bottom so that the sound rings out more. You might also find, as I definitely did, that lifting the dulcimer allows a better angle for both your fretting and your strumming hands.  Then again . . .  you might not. It's all a matter of personal preference.

It has strap buttons, so I thought I might see how that felt, to play with a strap. 

@carolynf, Cynthia is right that you will want to adjust your seat so that your lap is flat, either by lowering your chair or raising your feet. 

But another approach--which is not traditional but pretty common these days--is to use a strap.  When I first started I played in an office chair with adjustable arm rests that I could lower to hold down the dulcimer.  I realized it was ridiculous to learn an instrument that I could only play at my desk, so I installed strap buttons and immediately felt I had more control over the instrument.

Fabulous playing! I either use a shorter chair, or put my feet on my guitar case if the seat is too high. It's important. 

I love this mixolydian tune and that was a great arrangement you played. Welcome to the coolest site on the web.

I know I have short thighs, but never thought about how that doesn’t give as good a perch for the instrument as I’d like. The non-skid piece helps, but I may keep thinking of how to hang on to it better.

That's nice playing, @carolynf.  If this is how you start, I can't wait to see where your journey goes!

I decided to start with Sandy River Belle because I like it, know it on banjo, and it worked well figuring it out on my dulcimer. So fun!!