Accepted for publication on A&A LettersContext: Line asymmetries are generated by convective Doppler shifts in stellar atmospheres, especially in metal-poor stars, where convective motions penetrate to higher atmospheric levels. Such asymmetries are usually neglected in abundance analyses. The determination of the 6Li/7Li isotopic ratio is prone to suffering from such asymmetries, as the contribution of 6Li is a slight blending reinforcement of the red wing of each component of the corresponding 7Li line, with respect to its blue wing. Aims: The present paper studies the halo star HD 74000 and estimates the impact of convection-related asymmetries on the Li isotopic ratio determination. Method: Two methods are used to meet this aim. The fir...