(Shortened) Luminous blue variable stars (LBVs) form dust as a result of episodic, violent mass loss. To investigate their contribution as dust producers in the Magellanic Clouds, we analyse 31 LBVs from a recent census. We built a maximally complete multi-wavelength dataset of these sources from archival data from near-IR to millimetre wavelengths. We review the LBV classification on the basis of the IR SED. To derive characteristic dust parameters, we fitted the photometry resulting from a stacking analysis. For comparison we also stacked the images of low- and intermediate-mass evolved stars in the LMC. We find four classes of sources: 1) LBVs showing mid-IR dust emission plus near-IR free-free emission from an ionised stellar wind (Class 1a) or only mid-IR dust emission (Class 1b); 2) LBVs with a near-IR excess due to free-free emission only (Class 2); 3) objects with an sgB[e] classification; and 4) objects with no detected stellar winds and no circumstellar matter in their SEDs. From the stacking analysis of the 18 Class 1 and 2 objects in the LMC, we derived an integrated dust mass of $0.11^{+0.06}_{-0.03} M_odot$. This is two orders of magnitude larger than the value inferred from stacking 1342 extreme-AGB stars. The dust mass of individual LBVs does not correlate with the stellar parameters, possibly suggesting that the dust production mechanism is independent of the initial stellar mass or that the stars have different evolutionary histories. The total dust yield from LBVs over the age of the LMC is $sim 10^4-10^5 M_odot$. LBVs are potentially the second most important source of dust in normal galaxies. The role of dust destruction in LBV nebulae by a possible subsequent SN blast wave has yet to be determined. Recent theoretical developments in the field of dust processing by SN shocks highlight the potential survival of dust from the pre-existing circumstellar nebula.
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