From this sentence,
As an initial estimate I think we'll be looking at April to improve the existing system but for a new system it would take at least nine months.
Does it mean that the speaker will finish making the existing system completely better in April OR that he is going to begin improving the existing system in April and it will be finished sometime later?
To sum up, my question is what really is the meaning of the word "improve" used in this context.
The part of the sentence you should be focusing on is...
"... we will be looking at April..."
In this context, improve would to make the existing system better or more efficient. The way this is worded makes it sound like it will be started to be improved on April, and be more efficient at a later date.
If the goal is merely to improve the system, we're looking at an April delivery date; a new system would take nine months at least.
to be looking at is an informal way of saying "expecting, projecting, anticipating"
The projection can be time or cost, or even the details.
How much to repair the hail-storm damage to the roof?
-- We're looking at $6,000.
Why so much?
--Well, you're looking at demolition, a dumpster, roofing materials, labor to install the new shingles, etc.
When can you do the job?
-- We're backed up. We're looking at six weeks, at the earliest.
