Full disclosure, I work for Atlassian on our Premier Support team.
LFS tracked files are pushed over HTTP and stored in your shared home directory (i.e. your shared NFS storage). By design, that LFS push is happening away from internal git processes. From an architectural point of view you're just pushing a lot of binary data over an HTTP connection, which is being written to disk on the other end. Performance is bounded by your reverse proxy (which can probably handle mostly anything you throw at it), the Apache Tomcat webserver that Bitbucket runs (which can also handle most anything you throw at it), and the performance of your shared NFS server. Git processes aren't used to handle the data stream, which keeps processing overhead low.
Lastly, for whatever it's worth, I've never seen an LFS performance issue that wasn't the result of an external environmental factor (e.g. client side bandwidth limitations). You should be fine.