It would depend on the other rules of the universe, and the interdependence of the parts that are calculated in full fidelity with the parts that are lossily optimized. It is widely believed that events in our universe are affected only by events in their past light cones. If this is true, the computer or mind simulating our universe could postpone calculating a region of the time-space continuum, as long as that region is expanding at the speed of light. Once more processing power is acquired, or the demand for processing power is lowered, the computer or mind could "fill in" the empty region from the past to the future, until it catches up with the rest of the universe. Keep in mind, that if the universe is a simulation, it could be paused or slowed without affecting the laws of physics.

So to answer your question, you can calculate an incomplete but regionally lossless present state from an incomplete but regionally lossless past state, but you can't calculate a complete present state from an incomplete past state, if the present is truly dependent on past states.
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