I have found a problem in Paradox when using table names that are longer than 8 characters. If you have 2 table with names that are longer than 8 characters and the first 8 characters match, locking a record on one will be seen internally to paradox as a lock on both. So, I have a table named Minister and another named MinisterMP. They both have a number of records. If I go into edit mode on record 3 of Minister and then try to go into edit mode on record 3 on MinisterMP, I get a 'Record already locked by this session' error.
This only happens if the table is over a network. If it's on the local machine, there is no problem. My guess is that Paradox is getting the Short filename and using only the first 8 character. On the local machine is getting the dos 8 character name and on the network is the entire name. It may be a setting in the network. I found a reference to NtfsDisable8dot3NameCreation, when looking for short names. Microsoft suggest turning this on to increase performance.
So, if you get the Record already Locked message, check the table name.