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Since there is a closed form in the BS case for continuous barrier options, you probably won't find a huge amount of work on this since it's not needed. In the discrete case, I did a paper with Tang: http://ssrn.com/abstract=1441142 Pricing and Deltas of Discretely-Monitored Barrier Options Using Stratified Sampling on the Hitting-Times to the Barrier


LSM is very fiddly. The most important things in my view are 1) don't believe anyone who says that the choice of basis functions doesn't matter. 2) implement an upper bounder, eg Andersen--Broadie (2003) or Joshi-Tang (2014) so you can tell if your prices are good 3) do two passes, one to build the strategy, one to price, if they give very different ...

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