Someone asked me about a log transformation for their data. It seemed like a good idea, based on my general comments on the log transformation, but the test of significance for normality (Lilliefor’s test) was still rejected even after the log transformation.
In general, I dislike Lilliefor’s test (and other tests of normality like the Shapiro-Wilks test). They have way too much power power for large sample sizes and will often end up detecting trivial departures from normality. Instead of a formal test, use a histogram, boxplot, normal probability plot, or whatever to get a qualitative indication of how close your data is to a normal distribution.
Further reading
Steve Simon. Checking the assumption of normality. PMean blog 2002-09-11. Available in html format
NIST. Normal Probability Plot. Section 1.3.3.21 of the NIST/SEMATECH e-Handbook of Statistical Method, last updated in April 2012. Available in html format.