Tannins and lignins, which are natural phenolic compounds, are gaining substantial interest in biobased wood adhesive research. In this study, several different biobased tannin-lignin-hexamine adhesive mixtures were prepared and compared in a lap-joint shear strength test. In the first part, the suitability of different types of kraft and organosolv lignins as part of the mixture used in the production of biobased adhesives (in combination with pine tannins) were observed. It was found that biobased adhesive mixtures containing kraft lignins performed significantly better than those that contained organosolv lignins. In the second part, unmodified kraft lignins were mixed with pine tannin in different proportions, ranging from 0% to 100%. The pressing parameters were set to 150 °C for 15 min after performing oscillatory tests with a rheometer. Pure tannin adhesives performed the best, but no significant differences or a trend line were observed among adhesives containing different proportions of tannins and lignins.