The dust isn't on the lens — it's on the sensor. Dust on the lens will not resolve so clearly.
To check for it quickly, set your aperture to the smallest your lens can support. (Small apertures have large f-numbers, like f/22.) This will keep the light striking the sensor to a straighter angle, which in turn will make the dust (which sits on filter layer right above the sensor) resolve most clearly. Then, take a picture of something bright — plain blue sky is ideal.
Any dust should jump right out. In most cases, the built-in sensor cleaning will shake that off, but it's a reasonable idea to carry a (high quality) rocket blower if it needs a bit more. And if that doesn't work, make note of it (keep your test frame!) and resign yourself to touch-up in post
Note that the opposite to the above on aperture applies — if you shoot at wide apertures, any dust will be less apparent, and may even be completely hidden in some scenes. This is actually why the dust isn't apparent in the live view image on the LCD: what you see there is done with the lens wide open even when the aperture is set to close down for the picture. If you know already that you're dealing with this, you can plan to use a wider aperture so the dust is also less obvious in the captured image.