= Solution
The last lung-cancer failure before five years is at 4.85, where the displayed <net survival> estimate is 0.392. The other-death <net survival> estimate remains 0.498 from 4.096 until 5.065. Thus the two supplied curves imply \b[net five-year death estimates of $1-0.392=0.608$ for lung cancer and $1-0.498=0.502$ for other causes]. Their sum is 1.110, already showing that they cannot be probabilities of two disjoint actual causes of death.
In <competing risks>, let $\lambda_1(t)$ and $\lambda_2(t)$ be the <cause-specific hazards> while alive, with <cumulative hazards> $\Lambda_k(t)=\int_0^t\lambda_k(u)\,du$. Treating the other cause as censored estimates the <net survival> $S_k^{\rm net}(t)=e^{-\Lambda_k(t)}$. The actual probability of death from cause $k$ by time $t$ is the <cumulative incidence function>
$$
\boxed{F_k(t)=\int_0^t S(u)\lambda_k(u)\,du,\qquad
S(u)=e^{-\Lambda_1(u)-\Lambda_2(u)}.}
$$
Since $S(u)\le e^{-\Lambda_k(u)}$, the net probability $1-S_k^{\rm net}(t)$ generally overstates the <cumulative incidence function>: death from the other cause prevents a later death of cause $k$. This discrepancy exists even for independent latent cause-specific failure times. Moreover, Kaplan–Meier estimates are not generally exactly unbiased in finite samples even for their proper target. \b[The plotted complements are not unbiased estimators of $\mathbb P(T\le5,D=k)$, and are not even consistent for that target in general.]
For the desired probabilities, use the <Aalen–Johansen estimator> $\widehat F_k(t)=\sum_{u\le t}\widehat S(u-)d_k(u)/n(u)$, with all-cause survival $\widehat S(u)=\prod_{v\le u}[1-(d_1(v)+d_2(v))/n(v)]$ and independent study censoring. Removing competing deaths from subsequent <risk sets> is correct for estimating <cause-specific hazards>; the error is interpreting the separate <net survival> complements as <cumulative incidence functions>. A hypothetical elimination-of-a-cause interpretation of <net survival> would require additional causal assumptions.
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