What does the term 'lifetime' mean for electrolytic capacitors
The "lifetime" is the total time the capacitor can be in service while subjected to the maximum stresses specified in the datasheet, after which the manufacturer no longer promises anything about the cap.  In some cases, the manufacturer even tells you which parameters it no longer guarantees to what level.  Generally the ESR (equivalent series resistance) goes up.

Electrolytic caps wear out rather quickly at maximum voltage and temperature, but the higher the allowed voltage and temperature, the more possible uses, and therefore sales, there are for a capacitor.  Manufacturers are therefore stuck with a tradeoff of specifying low voltage and temperature or low lifetime.  Most of the time, they push the voltage and temperature and quote very low lifetimes, like 2000 hours (not even 3 months).

Notice that caps specifically sold as having a long lifetime have lower voltage and temperature specs for the same size case.

Lifetime goes up quickly as the voltage and temperature are lowered, although most datasheets unfortunately don't give you a lot of guidance on this.  A good rule of thumb is to keep the steady voltage on a electrolytic cap at about 2/3 of the maximum.  It's OK to go near the maximum occasionally, but don't ever exceed it.  Similarly, you want the steady temperature to be 20 to 50 &deg;C below the maximum.

The only way to get realistic lifetime values is to ask the manufacturer or find the rare cap where useful data on this is included in the datasheet.