Water is going to absorb O2 from the atmosphere. I don't think you'd gain as much letting the water sit overnight unless you either used a cap on the water (similar to mash cap or lauter cap) or filled the headspace completely with CO2 and sealed it with something. In either case I doubt you'd be transferring O2-free water. I've read someplace that the ability of water to hold O2 is inversely proportional to temp, i.e., boiling temps get rid of it, and the lower the temp, the more readily water will absorb it.
For that reason I like the boil it method then cool it approach better, as after I cool to strike temp (about 160 degrees) I'm not giving the water much time to absorb O2--into the mash tun it goes, underletting the grain.
Now, having said that--one reason we use sodium- or potassium-metabisulfate is to act as an oxygen scavenger, so it may not matter a lot if the water sat overnight as long as it was capped somehow. The water going into my mash tun isn't perfect, I'm sure, which is why the K-meta.
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How to cool that water has been an issue for me. I have a moderately-sized SS immersion chiller that I've used to bring the preboiled water down to strike temp. But it's hard to dial that temp in very closely as I've been using a Blichmann Hellfire burner which transfers residual heat from the burner to the kettle as it's cooling. I've made it work, but it's inelegant in terms of its precision. More than once I've overshot on the downside and had to restart the burner to bring it back up.
I'm switching to an electric brewery in part to control all this better. I've bought a SS counterflow chiller that I will use to bring that boiling strike water down to proper temps; by running the water through the lines while boiling I should purge the lines of air, and then I hope I can, while the water is recirculating, dial in the temp by controlling the chilling water going through it. We'll see. Hasn't been done yet, but in my mind's eye, this solves exposure to atmosphere as much as possible, should get me close to desired temp, and then when transferring to mash tun with pump, I should have cleared lines.
The other reason for electric brewing is to do a RIMS system to control mash temp. I'm not quite as concerned about nailing strike temp exactly because this should allow me to fine-tune that. I hope.
Those are the plans, in an attempt to further refine how I get that O2 out of the hot side.
PS: I've only been doing LODO stuff for about 9 months. I'm not expert, not by a long shot, so if anything I've written above is mistaken, please correct me. I think it's correct, or I wouldn't have written it, but doing LODO isn't a trivial exercise. At least, it hasn't been for me.
