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We study the importance of gravitational lensing in the modelling of thenumber counts of galaxies. We confirm previous results for photometric surveys,showing that lensing cannot be neglected in a survey like LSST since it wouldinfer a significant shift of cosmological parameters. For a spectroscopicsurvey like SKA2, we find that neglecting lensing in the monopole, quadrupoleand hexadecapole of the correlation function also induces an important shift ofparameters. For ${\Lambda}$CDM parameters, the shift is moderate, of the orderof 0.6${\sigma}$ or less. However, for a model-independent analysis, thatmeasures the growth rate of structure in each redshift bin, neglecting lensingintroduces a shift of up to 2.3${\sigma}$ at high redshift. Since the growthrate is directly used to test the theory of gravity, such a strong shift wouldwrongly be interpreted as the breakdown of General Relativity. This shows theimportance of including lensing in the analysis of future surveys. On the otherhand, for a survey like DESI, we find that lensing is not important, mainly dueto the value of the magnification bias parameter of DESI, $s(z)$, whichstrongly reduces the lensing contribution at high redshift. We also propose away of improving the analysis of spectroscopic surveys, by including thecross-correlations between different redshift bins (which is neglected inspectroscopic surveys) from the spectroscopic survey or from a differentphotometric sample. We show that including the cross-correlations in the SKA2analysis does not improve the constraints. On the other hand replacing thecross-correlations from SKA2 by cross-correlations measured with LSST improvesthe constraints by 10 to 20 %. Interestingly, for ${\Lambda}$CDM parameters, wefind that LSST and SKA2 are highly complementary, since they are affecteddifferently by degeneracies between parameters.

On the importance of lensing for galaxy clustering in photometric and spectroscopic surveys