How much lung cancer is really caused by smoking? On tobacco products one can often see the statistic that nine out of ten lung cancers are caused by smoking but is this number accurate?

I am sceptical about this stat for two reasons.
Firstly, if you compare cigarette consumption rates over time for the USA and Norway and compare them with male lung cancer rates you can construct the following chart. You can obtain cigarette consumption data for the US here and for Norway here and the cancer data for both countries from here.


In the USA it looks like 9 out of 10 lung cancers could very well be caused by smoking but in Norway it looks very doubtful because there is an awful lot of lung cancer for comparatively few cigarettes smoked. In the US the cause (cigarettes) comes before the effect (lung cancer) but in Norway the cause (cigarettes), seems to come after the effect (lung cancer). Which does not back up the hypothesis that smoking causes 9 out of ten lung cancers very well in the case of Norway.
In addition to the curiosity of Norway there is another problem because in a country such as the USA millions of people have been encouraged to quit smoking over decades and lung cancer rates have gone down. But in former soviet union countries millions of people have not been encouraged to quit smoking and as a result per capita cigarette consumption has been stable in these countries to this day. 

So quite by accident, we have a massive experiment (billions of subject years) to see if encouraging millions of people over many decades to quit smoking makes any difference to lung cancer rates. It is arguably, I would guess, the biggest experiment into smoking and lung cancer ever. Here are male lung cancer for three countries the USA (population 325.7 million ), Russian Federation (population 144 million) and Ukraine (population 45 million).

Clearly, male lung cancer has declined in these countries in the same way as in the US but without a preceding decline in smoking.
Secondly, in the US, according to the following National Health Survey , 17.9% of lung cancer occurs in never smokers, table reproduced below and original can be found here.

In my mind, the figure of 17.9% of lung cancer that occurs in never smokers makes the nine out of lung cancers caused by smoking as untenable. 
I would guess that to calculate this number all you really need to know is what percentage of the adult population are never smokers but I have found this number surprisingly elusive for the US. The closest I can find is in this study that states that in the US never smokers make up 22.2% of the population, current smoker 39.4%, former smoker 38.5%. 
But this can not be right and I think the authors have swapped current smokers with never smokers and that the number of never smokers is really 39.4% and the number of current smokers is really 22.2%. This is quite unsatisfactory but I have found it easy to find numbers for current smokers but difficult to find numbers for never smokers.
So having given a few relevant epidemiological statistics (and hopefully interesting to readers) as to why the number of lung cancers caused by smoking may not be quite as high as nine out of ten my question is as follows:
Given the statistics that 17.9% of lung cancers occur in never smokers and never smokers make up 39.4% of a population how much lung cancer is really caused by smoking?
 A: For the US data:
You are confusing two important but different concepts in epidemiology: prevalence and incidence. A Wikipedia page describes the difference.
The anti-smoking warning that you show says that 9 of every 10 lung cancers that occur are caused by smoking. That's the incidence of smoking-related lung cancers among all lung cancers that occur. Incidence has to do with how frequently in time cases of each type initially occur.
The Table 2 that you present, however, is for "age-adjusted prevalence" of smoking status among people who presently have each of the listed diseases. Prevalence has to do with the fraction of each type of case that is found at a given time. Of people currently having lung cancer, 17.9% have never smoked.
So why can't you say that "17.9% of lung cancer ... occurs in never smokers"? Because that's the prevalence of never smokers among those who are currently lung cancer survivors, not the fraction of all lung cancer cases that occur in never smokers. 
There's a big difference between prevalence and incidence here because smokers tend to die of lung cancer (and of other cancers, or from other causes) more quickly than never smokers. So at any given time, never smokers will thus be a higher fraction of all lung cancer survivors (prevalence) than their fraction in the total numbers of original cases (incidence).
For the Norway data:
What you present for Norway isn't directly comparable to the US data in terms of the relation between the risk of lung cancer and tobacco use, as you only show the use of manufactured cigarettes. The reference for cigarette consumption in Norway that you cite shows high use of self-rolled cigarettes and of pipe smoking (Figure 1 in that reference), with manufactured cigarettes representing less than 30% of Norwegian tobacco use until about 1980. These other forms of tobacco use aren't included in your graph for Norway, but would nevertheless be related to risk of lung cancer. In contrast, 75-80% of US tobacco use between 1955 and 2005, from your cited reference, was manufactured cigarettes. So you have to be careful with selective comparisons of tobacco consumption data, as manufactured cigarettes are not the entire story.
A: What you're asking about is called the "Population Attributable Fraction"—the number of cases in the entire population that can be attributed to the exposure (in this case, smoking). The formula for this is:
$$
PAF = \frac{P_{{\rm pop}}\times (RR-1)}{P_{{\rm pop}}\times (RR-1)+1}
$$
Here, $P_{{\rm pop}}$ is the proportion of exposed subjects in the population, and RR is the relative risk of developing the disease if you're exposed.
In the U.S., $P_{{\rm pop}}$ for smokers is $\approx 16\%$.
The RR for smoking is highly variable depending on what cancer you're talking about specifically, but using this document from the CDC, it appears the answer is $\approx 25$.  So, 
$$
PAF = \frac{0.16\times (24)}{(0.16\times 24)+1} = \frac{3.84}{4.84} = 0.793
$$
So that estimate you've linked to, which is effectively $0.90$ as their PAF, is a little aggressive. Though as @EdM notes, with a higher prevalence due to the time between smoking and developing lung cancer, you can get to a PAF of $0.90$ relatively easily.
