We carried out a multiwavelenght study of the black-hole candidate LMC X-3 with XMM-Newton .
The system showed a transition to a low-hard state , in which the X-ray spectrum was well fitted by a simple power law .
It then returned to a high-soft state , characterised by a strong disk-blackbody component .
The line-of-sight absorption column density is \buildrel { \lower 3.0 pt \hbox { $ < $ } } \over { \lower 2.0 pt \hbox { $ \sim$ } } 4 \times 10 ^ { 20 } cm ^ { -2 } , consistent with the foreground Galactic absorption .
This rules out wind accretion .
We argue that , despite LMC X-3 being a high-mass X-ray binary , Roche-lobe overflow is the main mechanism of mass transfer .
From UV/optical observations in the low-hard state , we determine that the companion is a slightly evolved B5 star with a mass M \approx 4.5 M _ { \sun } .
This is indeed consistent with the secondary star being close to filling its Roche lobe .