A lunar eclipse occurs when the Earth passes between the sun and the moon. As viewed from the earth, we see the Earth's shadow pass across the Moon. As viewed from the moon, we would see the sun go dark during the day, much like a lunar eclipse when the moon is viewed from the Earth. There would be some important differences though, due to the relative size of the Earth compared to the Moon, and the fact that the Earth has an atmosphere and the Moon does not.
When astronomers view a solar eclipse, what they are really doing is taking an opportunity to look at the "corona" of the Sun.
The Sun's corona is sometimes thought of as the Sun's "atmosphere" because it is highly variable, much like Earth's weather patterns, and because, being on the outside, it is most often what we observe. But if we were to observe the Sun's corona from the Moon during an event when the Earth passed in between, the appearance would take on not only characteristics of the Sun's corona, but it's interaction with the atmosphere of the Earth. The interaction of the Earth's atmosphere with sunlight is dependent upon the wave length or color of the light involved. During the day, we observe a blue sky because blue light has a greater susceptibility to scattering by the Earth's atmosphere, while red light passes more freely through air. As a result, when we view a sunset over water, when the Sun's rays are taking their longest path through the atmosphere to our eye, the appearance that we perceive is the red light, or the light remaining after the blue has been scattered.
Relative size between the Earth, Moon, and Sun is an inportant factor when considering how an eclipse might appear from the moon. The Sun is about 400 times the moon's diameter and about 400 times as far away from the Earth. This coincidence means that both appear about the same size, and thus neatly occlude each other during an eclipse.
The moon is about one fourth the earth's diameter, so when viewed from the Moon, the Earth would be about four times the size of the Sun. This means that the Earth could completely occlude the view of the Sun from the Moon, in fact turning the Moon completely dark, but we would visualize the interaction of sunlight with the Earth's atmosphere as the event occurred. This would most likely be a very colorful event, much like a sunset over the water looking west. That is, as the Earth's atmosphere scattered away much of the blue light, red light would be left to travel on to the moon, appearing like a red and orange sunset.
With these factors considered, the visualization of an eclipse event as perceived from the vantage point of the Moon is a good candidate for computer simulation. A computer generated model of an "Earth eclipse" would make a good science project, and even better poster or electronic wall decoration.