New lifters on old Cam

Depending on circumstances when re-assembling engines for a variety of reasons, generally one of which was simply to make them run again many old time mechanics used a straight edge to verify that the used lifter was still shaped more or less with a slight radius on the mating surfaces and that is convex not flat nor concave. While the procedure is arguably a proper one or not, it did verify the lifter would work more or less correctly thus forestalling an immediate failure.
That said?
Given the cam does not have lobes in a failure mode, there is no reason why a new lifter would not buy some time when using them.
It becomes a personal decision at that point in time.
Buying half way decent lifters in the first place are probably a good idea.
As Isky sends me a box of 16 Lifters when I order a cam for my I-6 engines, I have a couple of new lifters stashed in my spare parts sources. And if I thought I needed one, I would use one.
There is plenty of access to use assembly lube when doing so.

I had an 86 J10 I bought for cheap due to the engine leaking oil like a sieve, running out of oil, & sticking the 1 & 2 rod bearings to the crank. I pulled 1 & 2, & the crank. I had the crank turned, resized the rods, slapped it together with new bearings. It ran great, but would start ticking when warmed up. I pulled the intake & all the lifters. A few of the lifters were really dished bad, like 1/8" or more. I replaced them with cheap Summit lifters. Reassembled it with moly lube everywhere I could get it & started it following usual cam break in procedures. It ran great, even better than before the lifter replacement of course. I ran it for a few thousand very hard miles before I sold it & it held up fine. I saw the truck a few times over the years after I sold it, but never talked to the owner to see if he had any trouble with it.

I've never worried about it so I am probably no help to you at all, but I also never had an engine fail after I re-assembled one and started it.

Rotating the engine by hand will just spread the lube over the cam lobe, won't wipe much (if any) off. If the engine sits for a few days or weeks before starting enough lube COULD run off... depends on what type of assembly lube was used and how hot the storage area gets. Most assembly lube is "sticky" and will be fine for at least a week or so. But in hot area and an enclosed hot garage... enough could run off to be an issue over a day or two. Not many engines built in the hot desert areas in the dead of summer though... too hot for the builder!