My dogs tend to attack the mower rather than be frightened of it. Something about smaller engines. They are the same with motorbikes, mopeds, anything that makes a similar noise.
Attacking the mower as you try to mow the lawn is common in Border Collies which is what we have, lol.

Fear of sound often develops with age, pups and very young adults often being unaffected and, even though you hear about these desensitisation tapes that you play with the sound the dog is scared of, I don't think there is much that can change a dogs mind about a really loud sound like thunder or fireworks once they've developed the fear, especially as these sounds can be well loud enough to make the house shake which a tape can't replicate.
Keeping the dog indoors and not fussing around her all the time is your best bet during storms etc...have her own little hideout thats dark like a crate covered in a blanket so she can go and hide. They prefer somewhere smaller that is dark to hide during these types of situations. for certain situations like if you know a big storm is coming, maybe something from the vets to calm her down. Many pet owners get something for their pets here in the UK for Bonfire because of all the fireworks. Several evenings in a row that literally sound like the blitz from getting dark to midnight or later.

With the lawnmower, just allow her to keep away from it and don't make a deal because this can make fear behaviour even worse because you are either further convincing the dog that the sound is bad news or you are actually rewarding their fearful behaviour so they'll do it all the more for attention.