I am looking for any studies that involved twins that would show how much lifespan can be increased by living healthily, and how much it depends on lifestyle rather than genetics.
A few countries have large long-term databases and studies based on this data:
There are also lots of review articles on the subject, for example Genomics of human longevity.
Most of the studies seem to show an impact of about 20 to 33 percent from genetics, for example from the first study:
The heritability of longevity was estimated to be 0.26 for males and 0.23 for females
and the second:
Over the total age range examined, a maximum of around one third of the variance in longevity is attributable to genetic factors, and almost all of the remaining variance is due to nonshared, individual specific environmental factors.
and the review:
Heritability studies comparing the concordance of lifespan in monozygous and dizygous twins estimated a 25–30% genetic contribution to human lifespan variation
Basically, this means that they compared identical to fraternal twins, and found that the variability in lifespan between identical twins was less than that of fraternal twins. When also taking into account that fraternal twins share an average of 50% of their genetic material, the influence of genetics appears to be around a quarter to a third. The second paper I linked to above has some explanations on how they calculate this and what the numbers mean.
Drawing conclusions from twin studies to the overall role of genetics is not a completely exact science1, but this is probably the closest we can get to putting a number on this, I think.
1) There may be other reasons for this, for example identical twins choosing to lead similar lifestyles more often. This is mentioned in the second paper: "It is possible, for example, that this difference in risk is attributable to more similar environmental circumstances of MZ [identical] than of DZ [fraternal] pairs, rather than to their differences in genetic similarity."