While it's not a sure thing that you will puncture the tube if you use a tire lever to mount the tire, the risk is there and significant. Especially if you're on the road and only have one spare tube.

But you can use a "bead jack" to safely lift the bead over the sidewall without risking a puncture. VAR makes a combination bead jack/tire lever that is portable enough to carry with you on rides:



Kool Stop also makes a bead jack, but it's significantly larger than VAR's (and stiffer and better leverage as well), so it's better suited as a shop tool: