I’m taking control over a website in the next week or so. I am wanting to make sure i have a certificate in place before the migration. The current provider also uses Lets Encrypt, i want to make sure that when i do DNS verification on the domain name i won’t invalidate their current certificate, will this happen?
No. Issuing certificates doesn’t invalidate other certificates. Indeed, it’s normal to have multiple valid certificates at the same time, since that’s what happens when you renew a certificate before the previous one expired.
You can revoke the other certificate – if you want to shoot yourself in the foot, or after the migration is complete – but Let’s Encrypt doesn’t do it automatically, and as far as I know no ACME clients do it automatically.