I first encountered this term in a meeting I attended.
Q: We would like to be able to reverse the polarity of the neutron flow without requiring a reboot.
A: Yes, that is something we've been thinking about, but we don't have line of sight to having that feature before the end of the month.
From context, having line of sight to a result means something like "Have made it part of our immediate plans to achieve that result."
This appears to be extending the idiom on the horizon. Literally, something on the horizon. is at the edge of what can be seen. Figuratively, then, something that is on the horizon is at the edge of what can be predicted. And if something can be seen, then you have line of sight to it.
There is another aspect of line of sight: The view to the object must be unobstructed. Taking the analogy further, then, having line of sight to a result means that there is a plan for achieving that result that is not dependent on work from another team.
Note that I don't know if the "unobstructed" part of the analogy was intended by the speaker. All I have to work from is that one snippet of conversation.
In an attempt to obtain better insight into the phrase line of sight, I searched the intranet, and the hits fell into a few categories.
One category was people using the term literally, usually in the context of wireless communications.
Another category appeared to use the phrase as a synonym for "insight obtained from information":
Monthly tear sheets are improving line of sight.
Teams were empowered to reallocate expenses within discretionary line items, but there was a lack of transparency into these changes. Forecasting was a challenge because we did not have line of sight into these reallocation decisions. We will address this by developing a pivot tool that provides management a consolidated line of sight into spend by resource.
Note also the business jargony use of spend as a noun, meaning expenditure.
The third category appears to be what I heard in that meeting, where it means something like "a path to a result":
XYZ was impacted by ABC and DEF. We have line of sight to get back on track.
And then I think I hit the jackpot: Somebody defined the term, sort of.
Line of sight to ending year $XX under budget
XYZ is at 99% pass, with line of sight to ending the year at 100% pass. ABC is $YY under budget, and is on track to end the year at $XX under budget.
The value $XX was repeated both in the heading and in the body, which let me match the two statements. And one of the statements uses the phrase line of sight, whereas the other uses the more conventional phrase on track.
I therefore conclude that the two are roughly synonyms. Line of sight to X means on track to X.
Though this means that one of the citations above translates to "We are on track to get back on track," which sounds kind of eerily meta.
The preferred emphatic form of line of sight appears to be clear line of sight.