The 100,000 figure relates to non-covid deaths due to the pandemic, which does not necessarily mean the lockdown. For instance, this figure includes those who are dying from cancers and other diseases after delays to treatment, when earlier treatment may have saved their life.
This is not a response to lockdown. Lockdown would ease this to an extent, because lockdown reduces cases and allows some focus elsewhere. A lapse lockdown response would only increase these deaths, because it would mean more delays and more indirect deaths from delayed treatments. Delayed treatments are happening because of NHS being stretched due to the coronavirus, not lockdown, and as such deaths from this cannot be attributed to the lockdown.
Of course there are some deaths in there which will be due to the negatives of lockdown. Increased poverty, and the SAGE figure estimates 40,000 which can be attributed to things like mental health and poverty. However, this is over a 50 year estimate of the impacts. What we know is that coronavirus has cost 100,000 lives directly, and may have been more if we had looser restrictions. From this, the impact on deaths is predominantly from coronavirus and if we are to base it on saving lives alone then lockdown is only a benefit for reducing it.
Of course there are other issues…