Does lead lining really work against a nuclear explosion?

Obviously not:

In response to this claim, a civic-minded scientist has subjected the stunt to the rigors of scientific peer review and posted the results on Overthinking It, a blog with a tagline of “where we subject the popular culture to a level of scrutiny it probably doesn’t deserve.” After a careful and extremely thorough crunching of the numbers comparing drag, wind resistance, the energy and force of an atomic bomb blast versus a solid Frigidaire, Dr. David Shechner concluded that, sadly, it just wasn’t possible. Then he goes ahead and lists all the ways that beloved hero and professor of archaeology Indiana Jones would perish in the blast. In short, sorry George Lucas, but it’s back to digging the bomb shelter in the basement.

The linked blog delves into the protection lead would provide, and how the lead would actually be an issue itself:

Implicit in their implementation of this sequence is the authors’ belief that Indy’s survival is dependent on his encasement within the lead-lined refrigerator. However, this device itself may present additional dangers beyond those directly related to the atomic blast. To wit, the melting temperature of lead is a paltry 327.46°C, potentially below the external temperature. Now, liquifying lead requires enough energy to overcome its heat of fusion, and the time required to impart this energy. Observing the clip, we can only conclude that the air temperature exceeds lead’s melting temperature for a fraction of a second (and likely never reaches stainless steel’s melting temperature of >1500°C) though the ensuing nuclear furnace is probably warmer than a balmy Nevada afternoon. Temperatures near ground zero of the Hiroshima blast, for example, incinerated essentially any object that could be burned; the ensuing fireball ignited and consumed a substantially larger area. Hence, while it seems unlikely that Indy would find himself drowning in a pool of molten lead, it’s highly likely that the integrity of the lead lining would become severely compromised.

With regard to the shielding by lead:

He is, however, encased in a lead-lined refrigerator, which would provide some shielding from the massive onslaught of radioactivity. However, the efficacy of this shielding is questionable, since (1) lead shielding is all but useless against neutron radiation, potentially a substantial component of the radioactive flux, (2) the shielding’s effectiveness is proportional to its thickness: a full centimeter is required to reduce gamma radiation to half its initial intensity, ~3.3 cm are required to reduce it to 10% the initial flux and ~6.6 cm are required to drop the flux below 1% [Note the corrected math – see the comments section for this calculation. Thanks, Bunsen! -Ed], and (3) much of the lead shielding has probably been converted into a molten pool slogging inside the ‘fridge’s lining anyway (see above). Even if Indy manages to avoid receiving the acute lethal dose, he’ll almost certainly experience a host of perfectly horrific alternative effects.