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With a distance of 170 pc, PSR J2144-3933 is the closest isolated radio pulsar currently known. It is also the slowest and least energetic radio pulsar; indeed, its radio emission is difficult to account for with standard pulsar models, since its position in the P-Pdot diagram is far beyond typical "death lines". Here we present the first deep X-ray and optical observations of PSR J2144-3933, performed in 2009 with XMM-Newton and the VLT, from which we can set one of the most robust upper limits on the surface temperature of a neutron star. We have also explored the possibility of measuring the neutron star mass from the gravitational lensing effect on a background optical source.