Light sources for extreme ultraviolet Lithography (EUVL) are continued to face challenges in the demanding performance for high volume manufacture. Currently EUV and beyond EUV (BEUV) community are focused on the dual-pulse laser produced plasma (LPP) using droplets of mass-limited targets. These systems require extensive optimization to enhance the conversion efficiency (CE) and increase components lifetime that requires significant experimental and development efforts. We continued to enhance our comprehensive HEIGHTS simulation package and upgrade our CMUXE laboratories to study and optimize LPP sources and to make projections and realistic predictions of near future powerful devices. HEIGHTS package includes 3-D detail description of all physical processes involved in LPP devices. The models continued to be well benchmarked in each interaction physics phase of plasma evolution and EUV/BEUV production as well as in the integrated LPP systems. We simulated LPP sources in full 3-D geometry using Sn and Gd droplets and fragmented targets composed of microdroplets as a result of prepulse or from mist of tiny droplets distribution. We studied mass dependence, laser parameters effects, atomic and ionic debris generation, and optimization of EUV/BEUV radiation output, the requirements for mitigating systems to reduce debris effects. Our enhanced modeling and simulation include all phases of laser target evolution: from laser/droplet interaction, energy deposition, target vaporization and fragmentation, ionization, plasma hydrodynamic expansion, thermal and radiation energy redistribution, and EUV/BEUV photons collection as well as detail mapping of photons source location and size. Modeling results were benchmarked against experimental studies for the in-band photons production and for debris and ions generation.