EBS is basically a virtual storage area network from where tasks can be started. It can tolerate faults easily and users need not to worry about the loss of data even in case the disk damages in the RAID.
Provisioning and allocating the storage can also be done in Elastic Block Storage. If required, it can also be connected to the API. Lambda can accomodate with all the services provided by AWS. EBS being one of them and it has all the above said features. Hence, EBS works with Lambda absolutely fine.