They always talk about how there might be life on Enceladus, but how old is this lake really? I would imagine water being ejected from the moon is not a process that would last forever (because the water would reach an "equilibrium" in which it cannot be ejected). Since moon orbits can move, and planets change, it would not be unreasonable to imagine a time in which this process would not occur. But that leaves the question, how old is this lake? Its pretty important to know since if its young, there probably is no life, or just simple life. If it is old, then what has kept this process going, how long will it last, and is there life? (rhetorically; thats not the question).
I'm assuming you mean the underground ocean, as only Titan and Earth have actual lakes.
It's really hard to know the age of a geological feature, especially with limited opportunity to study it directly. Taking a photograph of the Moon doesn't really tell you how old it is, but getting samples of the Moon gives a pretty good idea. The best estimate to the age of Enceladus was published in Nature magazine. A few quotes:
The final exciting observation that comes from the model is that the amount of heat produced by the internal tide is sufficient to maintain Enceladus' subsurface ocean for billions of years
We know that it could be around for billions of years, and we know that it is now. There is some question as the age of Enceladus itself, which might only be 100 million years old.
Odds are that it's at least in the tens of millions of years, more likely billions. Geologically, it's been around for a long time. And in any event, it likely will remain around for some time.
I'm not sure that short of a sample mission that we could refine this any further, but it is an active area of research, so perhaps we will know more soon!
It might be that the 100-million-years estimate is much closer than the billions-of-years estimate.
Luciano Iess and his team are in the process of publishing a paper about the mass of Saturn's rings, based on Cassini radio science measurements. Those results were supposed to be sequestered until the paper comes out. But in a presentation at a planetary science meeting where there were members of the press present in the audience Luciano let some of it spill. His conclusion is that the total mass of Saturn's rings is significantly less than original estimates, and this points to "young" rings, certainly not as old as Saturn itself, and probably much younger.
Why does the age of the rings concern Enceladus? Models of ring formation include scenarios where the entire inner part of the Saturn satellite system undergoes "rearrangement", possibly with multiple collisions between moons that reform the satellite system essentially from scratch, and that rearrangement spawns the rings. Other similar scenarios put the age of the rings as young as 100 million years. But there has been much back-and-forth about this, with arguments between the "more than a billion" and "much less than a billion" camps, as mentioned here.
Rings don't naturally stay around unchanged. Viscous forces caused by particle-to-particle collisions make them spread with time. Particles that move outward and reach the Roche limit can coalesce into new moons; ones that move inward eventually enter the planet's atmosphere. Notably, the more massive the ring system, the longer it takes to fully disperse.
The recent measurement of low-mass rings suggests young rings. I can't wait until Luciano's paper comes out!
Another Cassini result is that the sub-ice ocean is global, not just around the south pole. The ice shell librates too much for it to be anchored to the core anywhere, and the only way to decouple it from the core is to have that ocean be global.