Of course they are suffering
Here is where it is essential to define suffering. When a car overheats would you say that the car is suffering? The point I am trying to make is we need to consider what is essential to meaning of suffering. Conscious experience is essential to what suffering is. We do not have any "experience meter" to determine what organisms do or do not have conscious experience. If the lobster being boiled alive does not have any conscious experience, then all its desperate struggling might appear to us to be a sign of suffering, but there would be no true suffering present at all. We do not know what it is like to be a lobster. Conscious experience, unlike physical phenomena, can be detected only firsthand. No one can detect or measure the conscious experience of another.
Lobsters may not suffer, but higher lifeforms for sure do. A harmed Insect trying to get away may do this because of primitive patterns of behaviour, which have evolved because they are usefull, but a dog, a monkey etc. we can recognize something that we understand and experience in them.
Yes, they may not suffer in the same way, but i doubt that they are feeling well in such situations.
Back to the main topic:
Yes, there is a large ammount of suffering in the natural world, mainly cause evolution works this way.
Evolution is a process that is not controlled by an intelligent force, it also has no real goal, it just happens to enable a species to survive in a special environment, and if that environment changes then it is possible that 90% (or 100%) of that kind will die, and only a small minority with the needed traits for survival, will remain.
Worshipping all the forces which we tend to call nature, as bening and "loving", like some people do, is almost one step dumber than believing the craziest religious nonsense. All these morons think they very well know what "god", or "nature" wants, so humans should not play god or mess with nature, not mentioning that nature messed up a million times before we came to be.
To end all suffering is a noble idea, better than the acceptance of it, or the brainless belief that it might have a meaning.
Soon we might be able to take evolution into our own hands, and adapt individualy, as we see fit, and not in a millenia long, painfull process.