The properties of light leptoquarks predicted in the context of a simple grand unified theory and their observability at the LHC are investigated. The SU(5) symmetry of the theory implies that the leptoquark couplings to matter are related to the neutrino mass matrix. We study the resulting connection between neutrino masses and mixing parameters and the leptoquark decays, and show that different light neutrino hierarchies imply distinctive leptoquark decay signatures. We also discuss low-energy constraints implied by searches for charged lepton flavour violation, studies of meson decays, and electroweak precision data. We perform a detailed parton-level study of the leptoquark signals and the Standard Model backgrounds at the LHC. With the clean final states containing a di-lepton plus two jets, the QCD production of the leptoquark pair can be observed for a leptoquark mass of one TeV and beyond. By examining the lepton flavor structure of the observed events, one could further test the model predictions related to the neutrino mass spectrum. In particular, b-flavor tagging will be useful in distinguishing the neutrino mass pattern and possibly probing an unknown Majorana phase in the Inverted Hierarchy or the Quasi-Degenerate scenario. Electroweak associated production of the leptoquark doublet can also be useful in identifying the quantum numbers of the leptoquarks and distinguishing between the neutrino mass spectra, even though the corresponding event rates are smaller than for QCD production. We find that with only the clean channel of μ+E/_T+jets, one could expect an observable signal for a leptoquark masses of about 600 GeV or higher.