For small $n$ Monte Carlo integration is not needed, so for example, <A HREF="https://www.jstor.org/stable/2334482?seq=1#metadata_info_tab_contents">Kolmogorov-Smirnov Tests when Parameters are Estimated with Applications to Tests of Exponentiality and Tests on Spacings</A> by J. Durbin for $n$ up to 100 (table 3).   

These exact results were used to construct the <A HREF="https://www.jstor.org/stable/2684019?seq=1#metadata_info_tab_contents">Graphs for Use with the Lilliefors Test for Normal and Exponential Distributions</A>. There are also analytical approximations, see <A HREF="https://amstat.tandfonline.com/doi/abs/10.1080/00031305.1986.10475419#.XKeNzS2B3OQ">An Analytic Approximation to the Distribution of Lilliefors’s Test Statistic for Normality</A>.