(Solar Shed guy here, I currently have 5kW of panel hung on my office, 10kWh of lead acid, 2kW of inverter, etc)

Unclear as to what you mean "off-grid for 24 hours" - do you need to be off-grid 24/7, or simply run a 2kW device for 24h after the power grid goes down?

Both are quite expensive, the second somewhat less so than the first (though still very expensive). You can probably do the second for under US$10k, probably not the first.

And depending on the use case, the suggestion of "Use a generator..." is very, very much the cheapest option for short term use.

Taking both options here, and going with hardware I would trust to do the job:

If you want to run a 2kW load for 24h after the grid goes down, are OK with charging from the grid, and simply need a really long term, high capacity UPS for infrequent use, your best bet will be something like an Aims Power inverter/charger or similar. I would go with minimum a 24V system for this, and for 2kW, you really should be up at 48V. Yes, I know there are 5kW 12V inverters, and, no, you really don't want to be dorking around with hundreds of amps if you can avoid it.

A 4kW Aims Power inverter/charger will comfortably run a 2kW load, and will charge the battery bank afterwards. At 48V, you'll need a minimum of 1000Ah at a 20 hour rate, and will probably want 1250-1500Ah. If you can at all avoid parallel strings with lead acid, do so. A bunch of battery strings in parallel just guarantees early death, because they won't charge equally over time.

You could use a Trojan SPRE 02 1255 or SIND 06 1225 to build a single string that would run the load, as long as they're warm. This will almost certainly be cheaper than lithium unless you've got a good source of scrap cells and want to build your own. However, this is really hard on the cells (running them down to 80+% depth of discharge), and they won't last more than a few years if they're getting cycled like that daily. If it's infrequent use, have a ball, it'll be fine.

Now, if you want to do it with solar, it becomes a harder question. How long does it really need to run, and do you care about a generator? "Sun is not a problem here" is a common claim, rarely backed by data. You never get clouds or storms? With well aimed panels, in winter, you may only have 6h of usable sun (unless you're using trackers) to generate your 48kWh daily use (plus some overhead for charging), so you're looking at about 10-12kWh, /minimum/ - and realistically, if you want to ride through cloudy days, you'll need far more. Or, you have to have an automatic generator start. Another option would be to have far more battery capacity so you can ride through a few more days, but then you run into the problem of having to have enough solar to recharge it. Practically, for fixed panels, to ride through winter, you're looking at 20-30kW of panel hung.

Something like a string of SIND 02 2450 would get you around 115kWh nameplate of battery, which might be overkill, but you won't drain it too deeply with normal overnight use, and you have capacity for two days of "no solar input" with the pack capacity. The pack will be 3.25 tons, give or take, but still cheaper than a similar capacity in lithium.

I would estimate a system cost in the US$50k-US$75k range in materials if you do it yourself, easily $100k if you're having someone else do it.

The right answer here is to either connect to the power grid, or figure out a way to reduce your loads when there's no sun. Running a 2kW on solar, 24/7, is doable, but it's a very, very expensive project.