We report on early results from a pilot program searching for metal-poor stars with LAMOST and follow-up high-resolution observation acquired with the MIKE spectrograph attached to the Magellan II telescope. We performed detailed abundance analysis for eight objects with iron abundances [Fe/H]<-2.0, including five extremely metal-poor (EMP; [Fe/H]<-3.0) stars with two having [Fe/H]<-3.5. Among these objects, three are newly discovered EMP stars, one of which is confirmed for the first time with high-resolution spectral observations. Three program stars are regarded as carbon-enhanced metal-poor (CEMP) stars, including two stars with no enhancement in their neutron-capture elements, which thus possibly belong to the class of CEMP-no stars; one of these objects also exhibits significant enhancement in nitrogen, and is thus a potential carbon and nitrogen-enhanced metal-poor star. The [X/Fe] ratios of the sample stars generally agree with those reported in the literature for other metal-poor stars in the same [Fe/H] range. We also compared the abundance patterns of individual program stars with the average abundance pattern of metal-poor stars and find only one chemically peculiar object with abundances of at least two elements (other than C and N) showing deviations larger than 0.5 dex. The distribution of [Sr/Ba] versus [Ba/H] agrees that an additional nucleosynthesis mechanism is needed aside from a single r-process. Two program stars with extremely low abundances of Sr and Ba support the prospect that both main and weak r-processes may have operated during the early phase of Galactic chemical evolution. The distribution of [C/N] shows that there are two groups of carbon-normal giants with different degrees of mixing. However, it is difficult to explain the observed behavior of the [C/N] of the nitrogen-enhanced unevolved stars based on current data.