Step 1: Recall the two broad routes used to convert biomass into usable energy. Bio-chemical conversion (anaerobic digestion, fermentation) uses microorganisms and enzymes to break down organic matter into biogas or alcohol. Thermo-chemical conversion (combustion, pyrolysis, gasification) uses heat, with or without a controlled amount of oxygen, to break the biomass down into heat, gas, oil or char.
Step 2: Compare their overall conversion efficiency. Bio-chemical routes work well only on wet, low-lignin feedstock and a large part of the input energy is lost as digestate or in slow microbial breakdown. Thermo-chemical routes convert a much larger share of the chemical energy in the biomass into usable heat or fuel gas in a short time, which is why they are generally rated as having higher energy conversion efficiency. So Statement (I) is correct.
Step 3: Look at lignin specifically. Lignin is a complex aromatic polymer that resists attack by the enzymes and microbes used in bio-chemical digestion, so it largely remains undigested in an anaerobic digester or fermenter. Thermo-chemical processes do not depend on biological activity at all, they simply apply heat, so they break down lignin along with cellulose and hemicellulose without any resistance problem. This makes thermo-chemical conversion clearly superior at decomposing lignin, so Statement (II) is also correct.
Step 4: Since both statements match the accepted understanding of biomass conversion routes, option 1 is correct. Option 3 fails because it wrongly marks Statement (II) incorrect, option 4 fails because it wrongly marks Statement (I) incorrect, and option 2 fails because both statements are in fact true.