Your first interpretation is correct
Fixed..means fixed quantity of money for fixed period of time at a fixed interest rate. Cannot add or remove from the account....if you do you will be penalised
Lump sum... you can add or withdraw when suits you..at a variable interest rate (but note some lump sum deposit accounts have a limited number of withdrawals so study that as well as the interest rate before setting it up). In this type of account you can add in more money when ever you want...but beware that some of these accounts have upper limits whereby interest rate may change
best of luck...hope this helps