* Condition: A used engine in good running condition will be significantly cheaper than a rebuilt or brand new one. A junkyard pull could be as low as a few hundred dollars, while a professionally rebuilt engine can cost thousands.
* Mileage: Lower mileage used engines command higher prices.
* Completeness: The price changes drastically depending on what's included. A long block (engine block, heads, crankshaft, etc.) will be cheaper than a short block (block, crankshaft, pistons), and both will be cheaper than a complete engine with accessories (alternator, power steering pump, etc.).
* Modifications: Modified LS1s can be more or less expensive depending on the modifications. High-performance builds will command a higher price.
* Source: Buying from a junkyard, private seller, or reputable engine remanufacturer will drastically affect the price.
Therefore, there's no single answer. You could find a used LS1 for $500-$2000, while a professionally rebuilt or new crate engine could easily cost $4000-$10000 or more. Expect to pay significantly more if you're looking for a high-performance or modified engine.