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Lumped-element superconducting resonators are a promising technology for their use in millimeter-wave observations and quantum computing applications that require large arrays of extremely sensitive detectors. Among them, lumped-element kinetic inductance detectors (LEKIDs) have shown good performance in the submillimeter band in several earth-based telescopes. In this work, LEKIDs for their use as millimeter-wave receivers of astronomical applications are presented. LEKID arrays using a thin bilayer of superconducting titanium/aluminum (Ti/Al), deposited on the silicon substrate, have been designed and fabricated. The design of a dual-polarization LEKID with the goal of detection at the $W$ -band for two orthogonal polarizations is described and a fabricated array has demonstrated absorption at ambient temperature. Also, an approximate design methodology of the coupling parameter for LEKIDs’ readout, essential for dynamic range optimization of the detector under millimeter-wave radiation, is proposed. In addition, the resonance characteristics and coupling factor of the fabricated superconducting resonators using high-quality internal factor $Q_{i}$ under cryogenic temperatures have been analyzed. The design guidelines in this work are applicable to other LEKID arrays, and the presented superconducting Ti/Al thin-film LEKIDs can be used in future receiver arrays in the millimeter bands. [ABSTRACT FROM AUTHOR]