That depends on what you mean.
Programming-wise, you can get an infinite number of lives if, for example, you just picked up a whole bunch of Dead Cats. In a normal game this isn't possible, but with cheats/mods you could.
Theoretically, Guppy's Collar can bring you back an infinite number of times as well. The probability of getting more than two or three lives out of it is pretty low, but still, it's possible to get hundreds, thousands, even millions of lives out of that item. Same thing with the Broken Ankh.
However, if we're talking practically, then the maximum number of lives that can appear on the life list is directly related to the number of life-reviving items in the game. In Rebirth, the maximum would be "x14?", which can happen while playing as Lazarus and collecting the following items: 1-Up, Ankh, Dead Cat (x9), Guppy's Collar, Judas' Shadow, and Lazarus' Rags. Additionally, while carrying the Broken Ankh trinket, you also have an additional 22% chance of reviving as Blue Baby once all your other lives run out.
In Afterbirth, you can also collect the Mysterious Poster trinket, which will revive you as the Lost when you die. This effectively bumps the max to "x15?", though the on-screen number will not change.