Restore MySQL DB from mylvmbackup to .sql dump

Backups of MySQL innodb databases are taken using mylvmbackup and the resulting backup contains the whole mysql folder as per example below:

ibdata1
ib_logfile0
ib_logfile1
mysql/
mysql_upgrade_info
database1/
database2/
database3/
performance_schema/
phpmyadmin/

The following recover option is used with mylvmbackup

innodb_recover=1
recoveryopts=--skip-networking --skip-grant --bootstrap --skip-syslog --skip-slave-start

We have a client that would like a .sql dump file from the "database1" backup. The database1 folder contains .frm, .ibd files and a db.opt file. Restore preference is without stopping MySQL as we have other databases in use but if there is no other way then a small downtime would be ok.

Various research suggests I need to recover the ibdata1 file along with the DB but I'm concerned changes to this file will affect the other live databases on the server.

What is the easiest way to do this?