The following code fits the three-parameter lognormal distribution to (right) censored or complete (uncensored) data in R.
The R code implements a fitting strategy proposed by Jerry Lawless in his 2003 book Statistical models and methods for lifetime data (pp. 187-188). A similar strategy is suggested by Terry Therneau in this comment.
For some data sets Lawless’ fitting strategy yields an unbounded likelihood. See this blog post for more information on the unbounded likelihood of a 3-parameter lognormal model.