Lactic acid is a molecule used abundantly in the food, cosmetic, and pharmaceutical industries. It is also the building block for polylactic acid, a biodegradable polymer which has gained interest over the last decade. Seaweeds are fast growing, environmentally friendly, and economically beneficial. The Rhodophyta, Kappaphycus alvarezii, is a carrageenan-rich alga, which can be successfully fermented into lactic acid using lactic acid bacteria. Lactobacillus pentosus is a versatile and robust bacterium and an efficient producer of lactic acid from many different raw materials. Bioreactor strategies for lactic acid fermentation of K. alvarezii hydrolysate were tested in 2-L stirred-tank bioreactor fermentations, operating at 37 °C, pH 6, and 150 rpm. Productivity and yields were 1.37 g/(L.h) and 1.17 g/g for the pulse fed-batch, and 1.10 g/(L.h) and 1.04 g/g for extended fed-batch systems. A 3.57 g/(L.h) production rate and a 1.37 g/g yield for batch fermentation operating with an inoculum size of 0.6 g/L was recorded. When applying fed-batch strategies, fermentation products reached 91 g/L with pulse feed and 133 g/L with constant continuous feed. For control and comparison, a simple batch of synthetic galactose-rich Man-Sharpe-Rugosa (MRS) media was fermented at the same conditions. A short study of charcoal regenerability is shown. A scheme for a third-generation lactic acid biorefinery is proposed, envisioning a future sustainable large-scale production of this important organic acid.