The sinusoidal modulation of excitation intensity and phase-sensitive detection of emission is ideally suitable for the accurate determination of the lifetime and intensity of lanthanide luminescence. In this work we elaborate on the general mathematical and instrumental techniques of the frequency-domain (FD) measurements in the low-frequency domain below 100 kHz. A modular FD luminometer is constructed by using a UV-LED as the excitation source, proper light filters in the excitation and emission paths, a photomultiplier with a fast preamplifier, and a conventional dual-phase lock-in amplifier. Starting from the set of linear differential equations governing the excited-state processes of the lanthanide chelates, an equation linking the luminescence intensity to the general form of the excitation modulation was derived. Application to the sinusoidal modulation in the Euler's exponential form gives the expression for the in-phase and out-of-phase signals of a dual-phase lock-in amplifier. It is shown that by using a relatively large number of logarithmically equidistant modulation frequencies it is possible to use the Kramers-Kronig relation for checking the compatibility of the out-of-phase and in-phase signals. As an example, the emission from two different europium(III) chelates were measured by using 200 modulation frequencies between 10 Hz and 100 kHz. In addition to the conventional transition between D-5(0) and F-7(2) levels emitting at 615 nm, also the emission from the transition between D-5(1) and F-7(1) levels at ca. 540 nm was measured. The latter emission was also measured at different temperatures, yielding the energy difference between the D-5(1), and D-5(0) levels. The relatively large number of modulation frequencies allows also an accurate determination of lifetimes and corresponding amplitudes by using an appropriate nonlinear regression method. Comparison of the time-domain and frequency-domain methods shows that the weighting of data is different and both methods have application areas of their own.