Well, reading your question, maybe you should read about reproductive strategies first, so yo know why there are some plants that last only till their first reproduction phase and others that live on and reproduce each year: http://en.wikipedia.org/wiki/Semelparity_and_iteroparity
If you don't have much time, though, here's the gist of it. Iteroparity is your regular reproduction strategy; you live long, and you can reproduce once every certain time lapse without much problem. Humans do it, most animals too, and a good deal of plants and such. Semelparity, though has a one-time reproduction event and when it's done, the organism dies. What is the point of it? Well, normally these organisms don't have a very high life expectancy, so in the end, it's better for them to put all their remaining energy in producing a lot of offspring in that reproduction event than saving some to continue living and be eaten not much later anyway. It's like betting all your money in your last card. There are a good number of plants that do this, along with some animals and most fungi, I think? Not sure about that last part.
So now on to Felarya, would these two strategies still apply? Of course they would. I would believe most giant specimens would be Iteroparous, since using such an amount of resources and being Semelparous would be a waste... but then again, we have Mantoids, which by origin (Mantises) should be Semelparous too. Exceptions confirm the rule, don't they? XD
Human and tiny-sized species, on the other hand, would be Iteroparous as well for the most part, and only some species of animals would be Semelparous, while I expect a larger number of plants to be as well. Not trees, of course, but other plants are. All yearly plants are called like that because they die after bearing fruit, which is good for us since they produce a lot of it, like cereals and vegetables. Well, the same applies to Felarya.
So, to answer the question, yes. In Felarya, there will still be a life cycle because even if ageing is not a problem by itself, being eaten is still something that poses a threat to their survival, and organisms with low life expectancy will probably develop Semelparous tendencies.
P.S.: All this talk about Semelparity is making me want to play Saya no Uta again.