A method for processing a biocomponent feedstock, comprising: exposing a feedstock containing from 15 wt% to 40 wt% triglycerides to a first catalyst in the presence of hydrogen, the first catalyst comprising either a supported Group VI metal sulfide catalyst or a supported Group VIII non-noble metal sulfide catalyst under effective deoxygenation conditions including a temperature from 230°C to 375°C, an LHSV from 0.1 hr -1 to 10 hr -1, a hydrogen partial pressure of 1.4 MPag (200 psig) to 2.8 MPag (400 psig), and a hydrogen treat gas rate of from 34 Nm 3 /m 3 (200 scf/B) to 1685 Nm 3 /m 3 (10,000 scf/B), for forming an at least partially deoxygenated effluent, the at least partially deoxygenated effluent having an oxygen content that is at least 40% less than the oxygen content of the feedstock, wherein the supported group VI metal catalyst is a catalyst that includes one or more group VI metals on a support and where group VIII metals are not present as part of the catalyst and wherein the supported group VIII non-noble metal catalyst is a catalyst that includes one or more group VIII non-noble metals on a support and where group VI metals are not present as part of the catalyst; separating the at least partially deoxygenated effluent to form a gas phase effluent comprising propylene and a liquid phase effluent, the liquid phase effluent comprising at least 10 wt% olefins; separating at least a portion of the propylene from the gas phase effluent; exposing the liquid phase effluent to an acidic catalyst under effective conditions including a temperature of 180°C to 250°C, a pressure of 2.1 MPag (300 psig) to 6.9 MPag (1000 psig) and a space velocity of 0.1 hr -1 to 10 hr -1 for oligomerization of at least a portion of the olefins to form a product effluent; and fractionating the product effluent to form at least a diesel product fraction and a lubricant base oil product fraction. exposing a feedstock containing from 15 wt% to 40 wt% triglycerides to a first catalyst in the presence of hydrogen, the first catalyst comprising either a supported Group VI metal sulfide catalyst or a supported Group VIII non-noble metal sulfide catalyst under effective deoxygenation conditions including a temperature from 230°C to 375°C, an LHSV from 0.1 hr -1 to 10 hr -1, a hydrogen partial pressure of 1.4 MPag (200 psig) to 2.8 MPag (400 psig), and a hydrogen treat gas rate of from 34 Nm 3 /m 3 (200 scf/B) to 1685 Nm 3 /m 3 (10,000 scf/B), for forming an at least partially deoxygenated effluent, the at least partially deoxygenated effluent having an oxygen content that is at least 40% less than the oxygen content of the feedstock, wherein the supported group VI metal catalyst is a catalyst that includes one or more group VI metals on a support and where group VIII metals are not present as part of the catalyst and wherein the supported group VIII non-noble metal catalyst is a catalyst that includes one or more group VIII non-noble metals on a support and where group VI metals are not present as part of the catalyst; separating the at least partially deoxygenated effluent to form a gas phase effluent comprising propylene and a liquid phase effluent, the liquid phase effluent comprising at least 10 wt% olefins; separating at least a portion of the propylene from the gas phase effluent; exposing the liquid phase effluent to an acidic catalyst under effective conditions including a temperature of 180°C to 250°C, a pressure of 2.1 MPag (300 psig) to 6.9 MPag (1000 psig) and a space velocity of 0.1 hr -1 to 10 hr -1 for oligomerization of at least a portion of the olefins to form a product effluent; and fractionating the product effluent to form at least a diesel product fraction and a lubricant base oil product fraction.