This article investigates standardized versions of the signed likelihood ratio test statistic for inference concerning the mean and percentiles of a lognormal distribution based on samples subject to multiple detection limits. The standardized versions considered are due to DiCiccio, Martin and Stern (2001). Computational algorithms are provided and numerical results are given to assess the performance of the proposed methods, and to make comparisons with competing procedures. It is noted that the standardized signed likelihood ratio test statistics provide accurate inference for the above lognormal parameters even for small samples that include non-detects resulting from the presence of multiple detection limits. Furthermore, in the context of hypothesis testing, they are seen to provide comparable or better performance in terms of power, compared to a test based on the generalized inference methodology. The results are illustrated using two examples on environmental applications.