Dr. Lipschitz is the most trusted child psychologist, to at least Didi and Chas and several other parents. When the two adults have problems with their kids, they frequently turn to the doctor for help. Dr. Lipschitz has a wide range of items bearing his name -- books, videos, a 1-900 phone number, portable online services via satellite, even a maternity hospital (where Dil was born).
He makes his first real appearance in A Visit From Lipschitz, while he enforced many of his beliefs and mannerisms, only Didi and Chas really paid attention. Many other characters such as Grandpa Lou, Betty DeVille, and others dismiss Lipschitz advice, saying he doesn't really know anything. In addition, in "A Visit From Lipschitz", it's shown that Dr. Lipschitz is somewhat of a free loader, by taking advantage of Didi's (and most likely, any fan's) hospitality by eating her food, taking showers at other people's homes when he is invited there and even helped himself to other things to make himself comfortable. It can also be seen that while Lipschitz may preach about knowing about what's best for children, he may not know a thing. As he tries several things to keep Chuckie and Tommy calm and behaved, they don't really listen to any of his techniques. When Didi goes off to bring back Stu, Chas, and Lou, Lipschitz soon finds out he was accidentally left with Chuckie and Tommy. When they realize he sees them, both cry and scream fearfully, thinking he is to be their new mother.
Lipschitz tries everything to no avail, realizing he can't calm them, he breaks down in a fit crying. As he does, both Tommy and Chuckie now believe he's not a mommy but a baby like themselves and then crawl down to play with him. When he realizes that's all the boys want, he laughs and joins in playing with them. After spending time with them he decides to redo some of his work and promises Didi that he'll send her his manuscripts for free. While Didi is honored, Lou and Stu could not care less. The one thing Lipschitz really loves to do is eat, as he is seen at the end of "A Visit From Lipschitz" turning his back during a photo to look for "cheese" (although "cheese" is just a phrase people say when taking photos). It is also possible that Lipschitz mostly cares for making money; in "Naked Tommy" Despite Betty scolding her for mentioning him, Didi tries everything and even calls Lipschitz's hot line to ask for personal advice about what to do with Tommy running around nude, only to find that he provided a recorded message of the same thing he wrote in his book and charged money for every minute she waited on his hot line.
Dr. Lipschitz is seen in The Rugrats Movie, though only through television screens and audio hearings at his maternity hospital. It's possible that he and Didi might still keep in touch as Didi's being taken into his hospital, she mentions that Dr. Lipschitz had promised her the all natural Tibetan Zen experience. His maternity hospital was shown to have various different rooms for different ways of child birth such as aquatic room or waterbirth and even the old country room (which Boris had said "In the old country, a woman had her baby in the potato fields and kept going").
You can find Dr. Lipschitz gallery here.