Hey there! I'm willing to be contradicted by someone with a source, but I believe two things are getting mixed up here.
I know I have heard/read that Hot Lips Houlihan was the inspiration for Miss Piggy--I found several sources on the internet that say so, but none that gave an actual quote from Jim Henson or Frank Oz or anyone else. But, growing up with the show and having an avid interest in it, I believe that this may have some basis in fact, simply because it was widely commented on. Keep in mind, though, that Miss Piggy was supposedly based on the character of Hot Lips, not the actress Loretta Swit.
I think the confusion over the Peggy Lee/Piggy Lee came from the fact that when Miss Piggy was originally conceived as a character, she had the last name of "Lee" added to her name. I believe this to be a purely auditory pun, as in "Hey, wouldn't it be funny for Piggy's last name to be Lee, as is Peggy Lee? Ha ha." But the last name of Lee was dropped fairly quickly in cannon, as was Piggy's assertation that her first name was really Pigathius. These anomalous facts show up in Muppet Central's fan fiction as well as numerous fan sites because, well, muppet fans like to show off the weird little things we remember--especially if they are contraditory or odd. Then, when people say, "Her name wasn't really Pigathius, was it?" then the triumphant fan can pounce and say, "Ah ha! She was, too! In the Muppet Show episode with...." (We are beginning to rival Star Trek fans in our mania for trivia.)
Remember, the Muppet Show wasn't the first debut of Miss Piggy. She originally appeared as a singer with Herb Alpert, and at that time wasn't even done by Frank Oz. (Oh, help me here, someone. Was it Fran? I KNOW I wrote this down somewhere, but can't FIND IT NOW!) Anyway, the Piggy that showed up to sing with Herb was not really the Miss Piggy that we saw later. The same puppet was used, and the same name, but personality-wise, it was a different, um, person--at least partly because Piggy had a different muppeteer sitting forward. (I sortof like to think of it like I think of all those different frogs that used to appear on The Muppet Show--they were certainly frogs, but they weren't really Kermit, even though some of them looked an awful lot like him. The real Kermit required Jim--and now, of course, Steve.)
Piggy--the real Piggy--didn't really appear until the first season of The Muppet Show during the glee club skit in which Kermit conducts a whole riser full of barnyard animals. Piggy steps out of the chorus--unrehearsed and unexpected--and takes Kermit by storm by taking over the song--AND declaring her exuberant and fathomless passion for him. This was the start of our girl, and Frank Oz was the genius behind it. Of course, Jim deserves lots of credit too, for marginally holding on to his composure when it happened and allowing the characters--not the actors--to determine what would come of this unexpected declaration. HIs style of leadership not only tolerated this sort of anarchy--it encouraged it and even celebrated it! And he managed to surround himself with people who weren't afraid of pursuing their own ideas about a character, but did it with respect for their fellow talent. This is collaboration of the highest order, and the hallmark of a true leader and a truly creative person. (pant, pant)
(Ru is stepping gingerly off her soapbox and slinking off to bed, where she shoud have been an hour ago.)