Ultra-metal-poor stars ($\rm {[Fe/H]} \lt -4.0$) are very rare, and finding them is a challenging task. Both narrow-band photometry and low-resolution spectroscopy have been useful tools for identifying candidates, and in this work, we combine both approaches. We cross-matched metallicity-sensitive photometry from the Pristine survey with the low-resolution spectroscopic Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) data base, and re-analysed all LAMOST spectra with $\rm {[Fe/H]} _{\rm Pristine} \lt -2.5$. We find that ~1/3rd of this sample (selected without $\rm {[Fe/H]} _{\rm Pristine}$ quality cuts) also have spectroscopic $\rm {[Fe/H]} \lt -2.5$. From this sample, containing many low signal-to-noise ratio (S/N) spectra, we selected 11 stars potentially having $\rm {[Fe/H]} \lt -4.0$ or $\rm {[Fe/H]} \lt -3.0$ with very high carbon abundances, and we performed higher S/N medium-resolution spectroscopic follow-up with the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) on the 10.4-m Gran Telescopio Canarias (GTC). We confirm their extremely low metallicities, with a mean of $\rm {[Fe/H]} = -3.4$, and the most metal-poor star having $\rm {[Fe/H]} = -3.8$. Three of these are clearly carbon-enhanced metal-poor (CEMP) stars with $+1.65 \lt \rm {[C/Fe]} \lt +2.45$. The two most carbon-rich stars are either among the most metal-poor CEMP-s stars or the most carbon-rich CEMP-no stars known, the third is likely a CEMP-no star. We derived orbital properties for the OSIRIS sample and find that only one of our targets can be confidently associated with known substructures/accretion events, and that three out of four inner halo stars have prograde orbits. Large spectroscopic surveys may contain many hidden extremely and ultra-metal-poor stars, and adding additional information from e.g. photometry as in this work can uncover them more efficiently and confidently.