Sometimes the data to be analyzed is not complete, and this may be due to censoring. There are two type of censoring, namely Type I and Type II. Whether the censoring was intentional or accidental, it is no guarantee that the data does not include suspected observations (too small or too large). Theses suspected observations might invalidate the estimate of the parameters of the model. One way to remedy this is to use trimming or Winsorizing. Traditional methods of estimation such as maximum likelihood, least squares, Bayesian, and moments methods, usually, work well for ordinary cases. However, these methods of estimations get affected seriously with outlier observations. This suggest using methods of estimation that utilize trimmed data, such as L-moment and TL-moment.  In this paper, we used six versions of L-moment and Trimmed L-moments with censored data for estimating the parameters of the Lomax distribution. The performance of the presented methods were compared with each other through a simulation study besides two real data sets. The results show that, for some cases, the use of Type-BD method is a better option than other methods. Our approach is similar to that of \cite{Zafrakou} which utilized the L-moments for the estimation of the parameters of a statistical distribution in the presence of censored observations.