Suicide is a very complex issue and as others have posted, it may take years for the full impacts of lockdowns to trickle through. Job losses, long-term uncertainty, not seeing family, continued anxiety and media stoking fears, etc. - all these will have impacts. In an ideal world the government would increase funding to MH services to forestall this, but the reality will be very, very different.
Another issue though is that using suicide as a proxy for mental health is crass and incredibly limited. Suicide is the worst outcome - but there are plenty of other forms of mental health suffering that will not show up in official data. Anxiety, depression, phobias, OCD, etc. are all difficult to track. And don't tell me that addictions - to alcohol, drugs, medications, overeating, internet-based (from pornography to gambling to gaming) have not been impacted - there is no data on these, or very little apart from referrals (and these are the tip of the iceberg), so ignoring this is a bit like the passengers on the Titanic saying 'Who cares about the ice cube over there, look at that starry sky!'
On the other hand, it would be good to see an assessment of the positive MH impacts of lockdown - I know personally that I have benefited from less crowds and rushing around, more exercise, and more time to do things like cook food and spend time with the kids (with obvious caveats).