We present results of new, deep Suzaku X-ray observations (160 ks) of the intracluster medium (ICM) in A1689 out to its virial radius, combined with complementary data sets of the projected galaxy distribution obtained from the SDSS catalog and the projected mass distribution from our recent comprehensive weak and strong lensing analysis of Subaru/Suprime-Cam and Hubble Space Telescope/Advanced Camera for Surveys observations. Faint X-ray emission from the ICM around the virial radius (r vir ~ 156) is detected at 4.0σ significance, thanks to the low and stable particle background of Suzaku. The Suzaku observations reveal anisotropic gas temperature and entropy distributions in cluster outskirts of r 500 r r vir correlated with large-scale structure of galaxies in a photometric redshift slice around the cluster. The high temperature (~5.4 keV) and entropy region in the northeastern (NE) outskirts is apparently connected to an overdense filamentary structure of galaxies outside the cluster. The gas temperature and entropy profiles in the NE direction are in good agreement, out to the virial radius, with that expected from a recent XMM-Newton statistical study and with an accretion shock heating model of the ICM, respectively. On the contrary, the other outskirt regions in contact with low-density void environments have low gas temperatures (~1.7 keV) and entropies, deviating from hydrostatic equilibrium. These anisotropic ICM features associated with large-scale structure environments suggest that the thermalization of the ICM occurs faster along overdense filamentary structures than along low-density void regions. We find that the ICM density distribution is fairly isotropic, with a three-dimensional density slope of –2.29 ± 0.18 in the radial range of r 2500 r r 500, and with –1.24+0.23 –0.56 in r 500 r r vir, which, however, is significantly shallower than the Navarro, Frenk, and White universal matter density profile in the outskirts, ρ r –3. A joint X-ray and lensing analysis shows that the hydrostatic mass is lower than the spherical-lensing one (~60%-90%), but comparable to a triaxial halo mass within errors, at intermediate radii of 0.6r 2500 r 0.8r 500. On the other hand, the hydrostatic mass within 0.4r 2500 is significantly biased as low as 60%, irrespective of mass models. The thermal gas pressure within r 500 is, at most, ~50%-60% of the total pressure to balance fully the gravity of the spherical-lensing mass, and ~30%-40% around the virial radius. Although these constitute lower limits when one considers the possible halo triaxiality, these small relative contributions of thermal pressure would require additional sources of pressure, such as bulk and/or turbulent motions.