When On the Lam is played the defender interrupts to preform a move which does not actually move the figure but simply gives it movement points equal to its speed.
The only reason On the Lam allows a figure to move out of line of sight of an attack is because when a figure gains movement points outside of their own activation the are forced to spend them immediately.
If a figure used On the Lam during its own activation it would gain movement points equal to its speed which would just enter its movement point pool instead of being immediately spent to avoid the attack.
For example, if a weequay attacks Han Solo, during its activation, and Han returns fire on the weequay and the weequay uses On the Lam, since it is during the weequay's activation it gains 4 movement points which enter its movement point pool and the attack resolves before the figure gets an opportunity to move out of line of sight of the attack.
Am I missing something or is On the Lam actually next to useless on your own activation?