When fitting a three-parameter lognormal model the likelihood may approach infinity (see figure below). This unboundedness of the likelihood occurs when the threshold parameter of the three-parameter lognormal model approaches the smallest observed failure time. A possible remedy, such that the likelihood becomes bounded again, is using the correct likelihood.
For some data sets it is necessary to resort to a remedy such as the correct likelihood. This is because the unboundedness of the likelihood might prevent a numerical optimization algorithm from finding the correct model parameters.
Example of an unbounded likelihood: The likelihood goes to infinity when the threshold parameter (=gamma) approaches the smallest failure time (marked by red line).
The following R code implements the correct likelihood for a 3-parameter lognormal distribution. The code may be used to fit the distribution to (right) censored or complete (uncensored) data in R.