Abstract New $^{12}$CO $J =$ 4–3 and $^{13}$CO $J =$ 3–2 observations of the N 159 region, an active site of massive star formation in the Large Magellanic Cloud, have been made with the NANTEN2 and ASTE submillimeter telescopes, respectively. The $^{12}$CO $J =$ 4–3 distribution is separated into three clumps, each associated with N 159 W, N 159 E, and N 159 S. These new measurements toward the three clumps are used in coupled calculations of molecular rotational excitation and line radiation transfer, along with other transitions of the $^{12}$CO $J =$ 1–0, $J =$ 2–1, $J =$ 3–2, and $J =$ 7–6 as well as the isotope transitions of $^{13}$CO $J =$ 1–0, $J =$ 2–1, $J =$ 3–2, and $J =$ 4–3. The $^{13}$CO $J =$ 3–2 data were newly taken for the present work. The temperatures and densities were found to be $\sim$70&x2013;80 K and $\sim$3 $\times$ 10$^{3}$cm$^{-3}$ in N 159 W and N 159 E, and $\sim$30 K and $\sim$1.6 $\times$ 10$^{3}$cm$^{-3}$ in N 159 S. These results were compared with the star-formation activity based on data of young stellar clusters and HII regions as well as midinfrared emission obtained with the Spitzer MIPS. The N 159 E clump is associated with cluster(s) embedded, as observed at 24$\mu$m by the Spitzer MIPS, and the derived high temperature, 80 K, is interpreted as being heated by these sources. The N 159 E clump is likely to be responsible for a dark lane in a large H II region by dust extinction. On the other hand, the N 159 W clump is associated with clusters embedded mainly toward the eastern edge of the clump only. These clusters show offsets of 20${}^{\prime\prime}$–40${}^{\prime\prime}$ from the $^{12}$CO $J =$ 4–3 peak, and are probably responsible for heating indicated by the derived high temperature, 70 K. The N 159 W clump exhibits no sign of star formation toward the $^{12}$CO $J =$ 4–3 peak position and its western region that shows enhanced $R_{4-3/1-0}$ and $R_{3-2/1-0}$ ratios. We therefore suggest that the N 159 W peak represents a pre-star-cluster core of $\sim$10$^{5} M_{\odot}$ which deserves further detailed studies. The N 159 S clump shows little sign of star formation, as is consistent with the lower temperature, 30 K, and has a somewhat lower density than N 159 W and N 159 E. The N 159 S clump is also a candidate for future star formation.