For example, Beverly pointed a Type-2 at Lore when he threatened Wesley, but then among those armed with Type-1's after Lore was beamed away.
True - and it's another example of the Doctor heading to danger armed, but apparently without calling for, let alone waiting for backup. But at least in "Conspiracy", we can speculate that Quinn used his flag privileges to jam communications so that Security would not arrive, and instead two bridge officers would come in and be disposed of, plus the unarmed CMO would arrive and be given a parasite to control her. In "Datalore", Lore would have no reason to, and no means of, jamming Crusher's communications.
IIRC, the scene in "Datalore" involved Beverly Crusher being the only one out of the initial three heroes to be armed at all, with that Type 2. The initially unarmed Lore then took the gun from her, after which she returned with Yar, Picard and Riker, the first armed with Type 2 and the rest with Type 1.
Which mainly raises the question of where Beverly got the gun in the first place, and why she didn't get one for Data. We know Sickbay has Type 2 in stock (it's a plot element in e.g. "Starship Mine"), but why would our trio go there, or to any other location with available phasers, and only take one rather than two or even three?
We could always argue that Crusher did take two guns, and Data's was of Type 1 and remained unseen in his belt. Perhaps Data did not initially want to use a phaser on his brother (as androids can't be merely stunned) and preferred to wrestle with him instead?