It's well established that the lag time is really between 2 and 5 months (papers galore on this topic). I was being generous/conservative by saying 2-3 months, just to emphasize the point.
Yes typical ENSO lag is something like 2 to 5 months. But it varies substantially on at least a seasonal basis. Development of nino 3.4 is often relatively steady from SH Autumn or winter, and typically peaks in Dec or Jan, and then decays reasonably steadily until next SH Autumn or Winter. In contrast global temperature shows zero response until October -lots of lag- , but then grows very quickly through Nov and Dec to peak at January - almost zero lag. It then drops a little early in the year but holds until May or June and then drops quite quickly so that September or October are pretty close to 0 ENSO influence in most years.
And from the data I've looked at I suspect bigger lag for stronger events, with 97/98 having the slowest and largest temperature response I've seen, and a couple short/small events below threshold el nino/la nina threshold coinciding with temp response at no noticeable lag. It does makes sense when you consider that inertia likely plays a role in the lag. The bigger the ENSO event, the longer it takes the climate to return to normal.
Geek warning: I'm a meteorologist, so this might get a bit technical. I'll try and just boil this down to the essentials.
It might seem like smaller events have a smaller lag or no lag, but that's very likely not to be the case. It's very likely you're looking at an outside influence or confounding factor. There's a very clear and physical reason for why ENSO takes a long time to have an effect. ENSO's effect on global temperature operates as a teleconnection through the tropical atmosphere and oceans. It essentially has to "drag" the entire tropical atmosphere and oceans with it, a process that is inherently long and drawn out, especially since the mixed-layer of the tropical ocean has a high heat capacity.
Once warm sea surface temperature anomalies appear in the ENSO region/ tropical Pacific in a more widespread manner, the atmosphere will attempt to compensate. The tropical atmosphere cannot sustain gradients for long, so it will attempt to dissipate them. The bigger the gradient generated, the faster it tries to compensate, and vice versa. The first is through deep convection. As the water warms relative to the atmosphere, it makes the atmosphere more buoyant and deep convection is more likely to result. The resulting convective overturning cools the surface of the ocean (through downdrafts and winds). That same convection releases latent heat aloft and the subsequent rising air over a large region results in increased subsidence and drying in adjacent regions, causing reductions in cloud cover.
As you might guess, this causes warming in those regions due to increased insolation. However, that warming takes a while (again due to high ocean mixed-layer heat capacity). Once enough warming has taken place, the subsidence and increased stability is compensated for and this feeds back onto the ENSO region, allowing warming there to continue and the cycle as a whole to continue. La Nina works in much the same way, though in (mostly) in reverse.
In this context, the argument of inertia doesn't really hold water. A weaker SST perturbation in the critical ENSO region results in a weaker gradient and weaker mass and heat compensation. The size and speed of the mass and heat compensation is directly related to the size of the gradient.
Sure, the seasonality angle does hold some water due to differences in climatological SSTs and their effect on convective thresholds (generally >27C), but in the case of this year, La Nina was in its traditional "season".
This does treat ENSO in a "vacuum".. of sorts. There are other outside influences that can affect and help drive (or hinder) ENSO of course, which are completely or mostly unrelated, but that kind of falls outside the boundaries of the current discussion.
I've oversimplified things here a bit, because mixed layer depths do matter somewhat, but my point is that there is no such thing as a "zero-time-lag" ENSO event. It can't happen. Even 2 months is stretching it a bit. The typical lag for ALL events is 3-4 months.
Ergo, this year is a Nina-cooled year and will likely remain so even if a decent Nino develops by September. It doesn't "average out". The only way to get that to happen is by having ENSO develop earlier in the year, like 2015 did (Apr-Jun).
Edits for clarification.