The approach the authors are using is Genomic Control (Roeder, 1999). The history of the use of GC in GWAS was (and is) that, in many cases, the inflation of the quantile-quantile plot is due to population stratification rather than bona-fide genetic association, so the statistic values can be adjusted to "correct" for that baseline level of inflation. The correction is simply multiplying the standard error of each variant by sqrt(inflation). However, one issue is that the observed inflation is really a combination of polygenic risk (e.g., quantitative genetic model) plus any population stratification; so subsequent refinements used other approaches besides the overall genomic inflation to estimate the contribution of population stratification.

In LD Score Regression, it turns out that the intercept of the model is an estimator of the contribution to association of pure population stratification, and thus can be used as a plug-in value for genomic correction.

In terms of how to achieved this: Multiply the standard errors by sqrt(lambda) prior to computing statistics and p-values.