Got to get to work but I would point out SHA-2 (commonly called SHA-256, SHA-384, and SHA-512) has not been broken, not even theoretically.

An attack on a reduced round version of SHA-2 has been found what this means is that SHA-2 uses 64 rounds (the input is passed through the same algorithm 64 times).  IF SHA-2 only used 42 rounds a faster than brute force attack would be possible.  However I would point out that the time complexity of such an attack is 2^251.  A brute force preimage attack on SHA-2 requires 2^255 operations so the "attack" is 2^(255-251) = 2^4 = 16 times more faster than brute force.   That still requires more time and energy than our solar system has to achieve a collision.

Lastly SHA-2 being partially broken (i.e. much faster than brute force attack) is not a concern when it comes to mining.  If miners using a modifed algorithm implementing the attack could mine 10,000 faster then it would simply mean difficulty would rise by a factor of 10,000.  If SHA-2 is broken completely then the issue isn't mining it is the privacy of the public key however LTC (and alll? alt-coins) use the same address structure.  This is less of a threat as addresses are the double SHA-256 and RIPEMD-160 hash of the public key.  It is unlikely both algorithms would be broken sufficiently to provide a credible threat.

The largest cryptographic threat to BTC (and by extension all alt-coins as they have copied this portion of the code bit for bit) is ECDSA.  Public key cryptographic is much harder to predict the likelihood that the cipher will remain secure.  Unlike hashing algorithms public key cryptography relies on an "unknown".  The strength comes from the fact that there is currently no feasible method of solving certain math problems.  If that assumption turns out to be false then the cipher will be vulnerable.  Through either cryptoanalysis or quantum computing I full expect ECDSA (and many other public key systems) to be broken wide open within my lifetime.  An alt-coin using an alternative public key system would provide an "insurance" policy of sorts but AFAIK none exist.