There’s no reason that a woman can’t continue to mow the lawn if she’s physically able to and it doesn’t go above her pre-pregnancy fitness routine.
According to ACOG:
Physical activity in pregnancy has minimal risks and has been shown to benefit most women, although some modification to exercise routines may be necessary because of normal anatomic and physiologic changes and fetal requirements.
In a low risk pregnancy, mowing is physical activity that isn’t outside your scope. As long as you take care to rest if you need to and stay hydrated and protect yourself from the sun, you can mow the lawn.
As with everything in pregnancy though, it depends entirely on whether you want to mow the lawn. If you find the noise or vibration isn’t easy to handle, or you have to mow a large area or on a hill, always take care of yourself and request that someone else does it – whether that’s your partner or a gardener.