Carbon stars have been and are extensively studied, given their complex internal structure and their peculiar chemical composition, which make them living laboratories to test stellar structure and evolution theories of evolved stars. They are the most relevant dust manufacturers, thus playing a crucial role in the evolution of galaxies. We study the dust mineralogy of circumstellar envelope (CE) of C-stars in the Large Magellanic Cloud (LMC), to achieve a better understanding of the dust formation process in the outflow of these objects. We investigate the expected distribution of C-stars in the observational planes built with the MIRI filters mounted onboard the James Webb Space Telescope (JWST), to select the best planes allowing an exhaustive characterisation of the stars. We compare the synthetic spectral energy distributions, obtained by the modelling of asymptotic giant branch stars and of the dust formation process in the wind, with the spectra of carbon stars in the LMC, taken with the Infrared Spectrograph (IRS) onboard the Spitzer Space Telescope. From the detailed comparison between synthetic modelling and observation we characterise the individual sources and derive the detailed mineralogy of the dust in the CE. We find that precipitation of MgS on SiC seeds is common to all non metal-poor carbon stars. Solid carbon is the dominant dust component, with percentages above $80%$ in all cases; a percentage between $10%$ and $20%$ of carbon dust is under the form of graphite, the remaining being amorphous carbon. Regarding the observational planes based on the MIRI filters, the colour-magnitude ([F770W]-[F1800W], [F1800W]) plane allows the best understanding of the degree of obscuration of the stars, while the ([F1800W]-[F2550W], [F1800W]) diagram allows a better discrimination among stars of different metallicity.
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