Nearby to what, it is important. Tenses within sumti are interpreted relative to the bridi. (CLL 10.13.) So, {lo vi broda} probably refers to something that is nearby to the place where the bridi happens at the time of the bridi happens. Few examples.
lo remna vu pensi lo vu dinju
Far away, a man thinks about a remote building.
The building is far away from the place of thinking, but may be the building which the speaker is in.
lo remna pu viska lo ca bajra
A man saw a runner.
The runner was running at the time it was seen by the man, but now may be resting.
and hence {lo pu broda} refers to the past broda
That would be undesirable in many cases. Most often we deal with present things. We cannot, for example, touch things from the past.
mi ca tavla lo pu bajra
I now talk to the one who was running.
It does not mean that I send my phrases into the past, so the runner in the past can hear me. The sentence does not say that there is a connection between the event of talking and the event of running. I just give a hint that the one I am now talking to was running. Suppose I know that the reader of my sentence saw that man running yesterday, so that would be a good hint.
Otherwise, {lo vi broda} would refer to something that is a broda on the
condition that it is close, and could morph into something else if it
happens to be somewhere else.
{lo vi broda} says that the referent, call it x, "fits" the first place of the selbri {vi broda}, i.e. {xy vi broda} is true. Let's use an example.
mi catlu lo vi mlatu
I look at a nearby cat.
{lo vi mlatu} says that the referent (x) is a cat that is near to the looker, the reference point of the bridi. Another cat (y) that is far away from me cannot be the referent of {lo vi mlatu}, because {.y bu vi mlatu} is false. The idea is not that x can morph into y, but that from x and y it selects x based on their location.