Heh, just happened to be reading another Lois Lane issue (#38, January 1963), and sure enough, there's another story about Lois with a signal watch, this time given to Lois by a phony Superman. Check out all the plot holes in this story:
Yep, a famous mobster left her a letter five years ago, but noble Lois and Perry haven't opened it, because, after all, the instructions said to wait five years.
But another mobster has long suspected that Gorcey had left information on the location of his loot with Lois, and has been bugging the Daily Planet for five years in the hopes that it would payoff eventually. So he gets one of his goons to have plastic surgery to look like Superman, and the fake gives Lois a signal watch, which will, of course, summon the mobsters when she locates the treasure.
So Lois opens the letter two days later, and learns the loot is hidden in a cave. She goes there to confirm it, and then signals "Superman" with her watch. When the crooks arrive, they start shooting:
Trapping Lois under debris. But (amazingly) the stalactites falling changed the frequency of the signal watch so that it summons Supergirl. She saves Lois and captures the crook. And at the end, they hold out hope that Lois may yet get a (third) signal watch:
I checked the next few issues, but there were no letters from readers clamoring for Lois to get her own means of summoning Superman.