It does not matter at all if anybody believes it was an unlawful dismissal if Scotland is anything like Canada.
It is super easy for a non-unionized company to cover their butts in a civil suit over an unlawful dismissal. All they have to do is come up with some documentation showing she was late a few times and she won't have a leg to stand on in court.
As long as the buyout was not a bonus that is owed to her, and its only a condition of a layoff they won't have to pay it because she was fired, not layed off.
Also, if she signed a code of conduct agreement and she broke that, its grounds for termination. They could also claim she could no longer be bondable as she claimed she was abusing her time remaining and waiting for money, which would like bad to a client who trusted her with their money.
Did the bank do something ethically wrong? Maybe, but thats just an opinion. Did they unlawfully dismiss her? Maybe they did that too, but welcome to reality land.
Not every country is like the US where sueing someone for making coffee too hot gets you cash.
Long story short, in the real world, you watch your Ps and Qs.