Immigration lawyer asking for payslips

Why would you do that? Are you trying to hide your salary?

If the immigration lawyer will use it for getting you visa, you might be charged for purgery. This is a crime with jail time.

You forgot to add /s

Never lie to immigration, they can rescind your status anytime if they figured the fraud

AFAIK it's fairly standard practice to submit payslips (as an indicator of being employed during previous periods) to the government, in support of an application to change/extend status or change employer. Blacking out the numbers will just be weird, your employer's lawyer will likely ask for unredacted versions to submit to the government.

Don’t worry about hurting your lawyers’ feelings. They make a good salary too.

I think OPs Intent is if the lawyer shares it with the new company - say you had added 10% 15% to the salary to the HR to negotiate better