If input data is monthly, LPJmL employs an internal weather generator to convert monthly to daily data. Temperature and cloudiness (or radiation) values are simply interpolated linearly, assuming that the provided monthly mean occurs on the day in the middle of each month.
For precipitation, monthly amounts can be distributed evenly across all days of that month or can be distributed to a number of wet days, using a stochastic weather generator that clusters precipitation events (i.e. rain is more likely if it also rained yesterday).

src/climate/prdaily.c
src/numeric/interpolate.c

Gerten, D., Schaphoff, S., Haberlandt, U., Lucht, W., Sitch, S. 2004: Terrestrial vegetation and water balance: hydrological evaluation of a dynamic global vegetation model. J. Hydrol. 286, 249–270.