Litecoin has recently updated the prefixes of their P2SH addresses to update address that begin with a '3' to addresses that begin with an 'M.' This change was made to stop confusion between BTC and LTC's P2SH addresses, which used to be able to have the same '3' prefix. This does not affect all LTC addresses, as the 'L' prefix LTC legacy addresses (Non-SegWit) will stay the same.
ShapeShift currently is able to send LTC to addresses that begin with an 'L' or a '3' only. At this time ShapeShift can only send to LTC addresses that begin with an "L" or "3"; we currently do not support "M" addresses.
If your wallet provider only creates the newer LTC addresses for your coins and you would like to use ShapeShift's services to receive LTC, we recommend getting a wallet from one of these integration partners we know that use ShapeShift compatible LTC addresses: Exodus.io Jaxx.io or Coinomi.com