As an industry we seem to swing between briefing everything and then briefing nothing. At the end of the day (and as said above) threats requires mitigations. If you can't identify a mitigation strategy or the mitigation requires test-pilot abilities, then the threat is not worth talking about or you shouldn't be going flying. If SOP covers the threat as a normal component of your operation, it may not be worth talking about given the company has already told you what to do. I caution pilots not to brief themselves into an error caused by expectation bias, which unfortunately occurs not too infrequently through detailed briefings. That's why we say 'briefing' - it's meant to be a brief overview of what we are going to do, leaving us mentally nimble enough to react to the inevitable changes that come with day-of operations.
Let me first use a real-world example from yesterday. We landed a Max-8 with one reverser inop. The inclusion in my briefing was very short on the matter: "I will not select the #2 reverser, you will not see the REV indication on #2, and I plan to exit a D5." It's a threat that was mitigated an hour earlier when we set speed bugs for Flaps 40 and Autobrake 3 and I identified the extra distance needed required the next exit down. I did not need to add any of that to my briefing because they're already set and identified, so I only brief the differences that we will see on landing in as short-and-sweet a way as possible.
In the case of your low visibility operations example, there are 4 considerations: airplane, airport, alternate, and aircrew. Are there any MELs that affect your ability to conduct LVO; are there are NOTAMS that invalidate the LVOP; does your flight plan have a valid takeoff alternate that meets the minimum weather requirements; and does the crew meet the minimum experience requirements laid out by the ops manual? These are considerations that your instructor may want you to say aloud to ensure you're thinking about them, but unless they play a factor in your flight on the day, they're often not worth adding to your briefing. That's not to say don't discuss it with your co-worker, but not during the briefing. The lack of a takeoff alternate or a NOTAM that invalidates the LVOP should be discussed outside of the briefing. They are threats, but ones that should have been captured and mitigated far before your takeoff briefing such that once resolved, they no longer require discussion.
As for single runway ops. That happens all the time, and I wouldn't brief the lack of another runway as being a specific threat. What might warrant discussion, however, is that the closure of a runway may lead to other issues: high intensity operations or the need for a non-standard taxi route, especially at airports where coded taxi routes are used.
For this scenario (low vis with single runway ops) I would brief that we'd complete the taxi checklist and before takeoff checklist to the line before we begin our taxi so that we're both heads up during the taxi. I'd brief it because doing so goes against the procedure normally used standard visibility, I don't want it coming as a surprise to my co-pilot when I call for those checklists. If we also had a bleeds off takeoff, I'd ask my co-pilot if they had the supplementary normal checklist for bleeds off takeoff ready. That's as far as I'd take it. They've been trained on it, I've confirmed they know about it, no need to make it a big topic.
If at the end of the it is perfectly acceptable to say "No threats."