In the frequency-domain measurements of luminescence, the excitation intensity is modulated sinusoidally and the emission detected using a phase-sensitive amplifier. The present availability of conveniently modulatable light sources, such as light-emitting diodes and diode lasers, and relatively inexpensive lock-in amplifiers makes this technique well suited for the determination of lanthanide luminescence. The mathematical theory of luminescent lanthanide systems involves the application of matrix and complex analysis to the set of linear differential equations of the rate processes. The general solution is derived for the temporal populations of the excited species in the presence of an arbitrary functional form of excitation. The sinusoidal excitation and dual-phase lock-in detection of the emission provide a signal which can be expressed as a complex quantity with real and imaginary parts. It is shown that the imaginary part of the signal, i.e., the out-of-phase signal of the lock-in amplifier, is less prone to the interference from organic prompt fluorophores and external sources. The Kramers–Kronig relation can be used for checking the mutual compatibility of the real and imaginary parts of the signal. Two examples are given for the instrumentation and data treatment. The first example is the resonance energy transfer from a europium chelate to an organic acceptor held at a constant distance from the donor by oligonucleotide hybridization. The second example deals with the upconversion material, a mixture of lanthanide compounds. In both cases, the signal-to-noise ratio is excellent, allowing even the estimation of the continuous lifetime distribution.