How to access an LDAP user account when disconnected from the work network

As far as I can tell from the steps you describe you appear to have successfully linked a client Mac to an LDAP server and this is proven by your being able to successfully login to the Mac using LDAP account credentials.

However I see nothing listed in your post that shows you have told the client Mac it should create a mobile account on the client Mac when you do an LDAP login. This is an extra step. Historically this was done by adding the computer to a managed group list in Workgroup Manager - this uses an approach called mcx for managed preferences. These days a similar but different method is to enrol the client Mac in to an MDM system and the MDM system would then push out a profile containing the equivalent setting. This setting tells the client Mac to create a matching local account which will be synced in terms of username and password to the ldap account. (It does not sync the users home directory.)

Here is what the relevant setting looks like in Apple's Profile Manager. (It is under the heading of Mobility.)

Without the client Mac having created a matching local account i.e. mobile account then there is no account available to login in to when you are not connected to the LDAP server.

It would be helpful to know which LDAP server you are using.