Can I convert an old dual fuel Electric/Propane range into a cooktop only that uses 120V instead of 240V?
Many people have one or more 240V outlet in the garage (shop tools, welder, etc.,) and many more will as electric vehicles (and associated chargers) permeate the marketplace more.
Anyway, if you don't, certainly the simplest option is to light with a lighter.
If the igniter circuit works from 120V (which you appear to assume, but I don't), and both the clock (where that assumption is more valid, IME) and igniter circuit are on the same leg of the 240V line, it should be possible (with care) to determine which leg of the 240V feed that is, and to wire a 120V plug to the line, Neutral, and Ground for that purpose - whether that's going to be a technical code violation or not, I don't know. If the current range cord is a 3-wire, you'll need to separate the neutral and ground, for sure.
You will need to take care that the other side of the stove's line connection is well-isolated, as that will be energized when someone unfamiliar with your modification tries to use the oven, unless you make more internal modifications to disable that.