LFGs can be implemented very easily in parallel, by just running independent generators with different seed tables on different processors. This works very well provided the seed tables are set up to be independent and uncorrelated. If not, any correlations can persist throughout the simulation. The seed tables should be initialized using a different generator, such as a parallel linear congruential generator.
The problem with this simple approach is that it will give different results on different numbers of processors. Can avoid this by having a different generator on each virtual or abstract processor, i.e. each element of a data parallel array (e.g. in HPF or CMFortran). However this requires a lot of memory to hold the lag table (which must be large for good randomness properties) for each array element, which can be infeasible.