A couple of years ago I was at a wedding where I got talking to another guest, who turned out to be a Rugby agent.
One of his clients was worth a few pounds (there's a clue there), and during our chat he told me that if a team had not even started to talking about a new contract by August, then they would assume the Club was not too concerned, and start "sounding out" other alternatives so that, in the case of English teams. they could officially agree terms in January. When it came to overseas teams they could start talking at any time.
I would have thought this was the way all agents operated, but if Lima's agent is based in NZ then he could well not be used to dealing with English clubs.