Although standard moments (such as the mean, variance, skewness, and kurtosis, etc.) may well characterize data, L-moments are increasing in popularity. Created about 28 years ago by J.R.M. Hosking, L-moments are linear combinations of order statistics and as such are less susceptible to outliers. L-Moments have been shown to uniquely characterize a given distribution and exist even when traditional moments do not. Although L-Moments have nice properties and have enjoyed increased usage across multiple fields, sample size requirements to estimate L-moments have not been established. The purpose of this work is to provide guidance on the appropriate sample size required to estimate the L-moments for several distributions such as Student's T, Normal, Generalized Pareto, Exponential, and Gumbel. Simulation Data will be generated for each of these distributions across a range of sample sizes and the resulting bias and variance compared to determine a reasonable sample size which results in an acceptable minimized MSE. These results may be used as a first step in the planning for studies which seek to estimate and test phenomenon based upon characteristics of the L-moments.