Can we solve for lambda in R? Assuming a poisson distribution, is there a way to solve for lambda in R?
My inputs would be "x", and Pr(X<=x) ... and I would like R to tell me the lambda.
Thanks

Is this what you're asking?
Suppose you are given $x = 7$ and $P(X \le 7) = 0.8666283,$ and that $X$ has a Poisson distribution, but you are not given that $\lambda = 5.$ As follows:
p = ppois(7, 5); p
[1] 0.8666283

Then a grid search in R can retrieve $\lambda = 5$ with the desired
accuracy.
lam = seq(.5, 20, by=.001)
pp = ppois(7, lam)
d = abs(p - pp)
mean(lam[d==min(d)])  # 'mean' in case of multiple hits
[1] 5

Addendum: Of course, @whuber's method, using
a related gamma distribution, is preferable
to a grid search for this problem (see comment). But such
identities are not always available for 'reconstructing' a parameter.
Here is an additional example using a grid
search for unknown binomial $n.$ Suppose
you know that $P(X \le 7) = 0.5618218$ for binomial $X$ with $p = 0.6,$ but don't know
$n = 12,$ as below in R:
p = pbinom(7, 12, .6);  p
[1] 0.5618218

Then you can retrieve $n$ as follows:
n = 2:50
pp = pbinom(7, n, .6)
d = abs(p-pp)
n[d==min(d)]
[1] 12

