Calculate sets of possible lognormal parameters given only a .95 quantile value Given a known 95th percentile value of $n$, and assuming a log normal distribution, is there a way to calculate pairs of possible parameters (meanlog, sdlog)?
I was able to get fairly close numerically, with n = 95:
lim95 <- 95
t <- 1000

find.sd <- function(lgmn,q95){
    x <- (seq(0,50,length=10000))
    lsds <- qlnorm(.95,lgmn,x)
    r1 <- x[min(which(lsds>q95))]
    return(r1)
    }

lgmn1 <- seq(0,4.54,length=t)
lgsds1 <- sapply(lgmn1,find.sd,q95=lim95)
test1.q95 <- qlnorm(.95,lgmn1,lgsds1)
cbind(lgmn1,lgsds1,test1.q95)


x <- seq(0,lim95*1.2,length=t)
y <- matrix(ncol=length(x),nrow=length(x))

for (i in 1:length(lgmn1)){
    y[i,] <- dlnorm(x,lgmn1[i],lgsds1[i])
    }


matplot(x,t(y)[,c(seq(1,t*.95,by=20),(t*.95):t)],type="l",col="red",
    lwd=.2,lty=1,ylab="",xlab="",
    main="Possible Log-Normal PDFs with 95 percent values of n=95")
abline(v=lim95,col="blue",lty=4)


I'm looking for a more generalized approach - numeric or analytical.
 A: We say that a random variable $Z$ has a lognormal distribution with parameters $\sigma\gt 0$ and $\mu$ when its logarithm, suitably standardized, has a standard Normal distribution $\Phi$.  That is, for any $z$,
$$\eqalign{
F_{\mu,\sigma}(z) &= \Pr(Z \le z) = \Pr(\log(Z) \le \log z) = \Phi\left(\frac{\log z-\mu}{\sigma}\right) \\
&= \int_{-\infty}^{\left(\frac{\log z-\mu}{\sigma}\right)} \exp(-t^2/2)\mathrm{d}t.
}$$
Equivalently, writing $\log z=\mu + \sigma y$,
$$F_{\mu,\sigma}(e^{\mu+\sigma y}) = \Phi(y).\tag{1}$$
Let $\alpha=95/100$ denote the number corresponding to the given percent.  The $\alpha\times 100$ percentile of $Z$ is the (unique) number $z_\alpha$ for which 
$$\alpha = F_{\mu,\sigma}(z_\alpha).\tag{2}$$
Writing $z_\alpha = e^{\mu + \sigma y_\alpha}$ in $(2)$ and applying $(1)$ gives
$$\alpha = \Phi(y_\alpha),$$
with the (unique) solution
$$y_\alpha = \Phi^{-1}(\alpha);\\ \log z_\alpha = \mu + \sigma \Phi^{-1}(\alpha).\tag{3}$$
Given $\alpha$ and  $z_\alpha$, equation $(3)$ defines a line in the $\mu,\sigma$ plane orthogonal to the direction $(1,\Phi^{-1}(\alpha))$, with $\mu$-intercept $\log z_\alpha$.  The portion in the upper half plane $\sigma \gt 0$ (which will be an open ray) describes all the Lognormal distributions consistent with this information.


These plots show (part of) the locus of $(\mu,\sigma)$ for the case $\alpha=0.95$ and $z_\alpha=2$ at the left.  The black dots indicate particular values of $(\mu,\sigma)$ lying along this ray.  At the right of each is the graph of the PDF of the corresponding Lognormal distribution, filled in to include a total probability $\alpha$. As intended, the filling terminates at $z_\alpha$ in all cases.
