Suppose I draw $n$ samples of some random variable $X$. I repeat this process $k$ times so that I end up with $k \times n$ observations.

Each time I draw a random sample, my data is censored, meaning that I cannot observe values larger than some maximum value. Specifically, the values observed is bounded from above by $c_i$ for $i \in 1,…,k$, each time a sample is drawn, where $c_1$, $c_2$, … $c_k$ can be any positive real value.

We know that $X$ follows a lognormal distribution with parameters $\mu$ and $\sigma$.

How do I estimate $\mu$ and $\sigma$ with this censored data, with arbitrary upper bounds $\{c_i\}_{i=1}^k$?

We can suppose that we know the support of $X$.

I looked at this source about censored data, but its prescriptions are not clear:

If all observations are censored, the MLE is undefined when there is a single censoring limit and defined but extremely poorly estimated when there are multiple censoring limits. The best approach for such data is to report the median, calculated as the median of the censoring levels (Helsel 2012, p. 143-4)

I guess this suggest taking the median of $c_1,…,c_k$?