Monthly data from the Victorian Suicides Register shows that until the start of September 2020, there had been no increase in suicides in the state compared to previous years
https://www.coronerscourt.vic.gov.au/sites/default/files/2020-08/Coroners%20Court%20Monthy%20Suicide%20Data%20Report%20-%20Report%201%20-%2027082020.pdf https://twitter.com/Paul_Karp/status/1320930338495868929

Of course, this does not preclude a large increase in September/October, but at least using the best current evidence there does not appear to be evidence to support the claim that policy has driven a direct increase in suicides

I have just found the more recent Coroners report showing that this trend persisted in September - again, it is possible that there was a large increase in Oct, but currently no evidence of an increase in suicide rates in Victoria in 2020 https://www.coronerscourt.vic.gov.au/sites/default/files/2020-08/Coroners%20Court%20Monthy%20Suicide%20Data%20Report%20-%20Report%201%20-%2027082020.pdf

This is in line with international evidence, which has failed to find a strong link between lockdown policies and suicidality https://www.medrxiv.org/content/10.1101/2020.10.20.20215343v1?%253fcollection=

Also worth pointing out that this does not preclude the lockdown causing mental health issues such as depression

Moreover, population statistics do not speak to the individual experience - it can be true that a single person's suicide was caused by the lockdown and that it has not caused an increase in suicide more broadly (perhaps because it prevented some suicides as well)