The money deposited by a person in a bank is, by its nature, subject to Zakāh if it reaches the niṣāb (minimum threshold), whether on its own or when combined with other Zakātable assets. Under normal circumstances, the depositor owns this money fully and has the ability to dispose of it by withdrawal or transfer. In such cases, Zakāh becomes obligatory upon reaching the niṣāb and after the completion of a ḥawl (lunar year).
However, if the bank has placed a full hold on the funds or severely restricted the amount that can be withdrawn, then this money is considered māl maḥjūr (withheld property). In this case, Zakāh is only due when the money is actually received, even if it remains with the bank for several years.
Therefore, the money you described in Lebanese banks is not subject to Zakāh unless you are able to withdraw it freely. If the bank has imposed withdrawal limits and restrictions on access to the rest of the funds, then the condition of full (or constructive) ownership is no longer fulfilled due to the ḥajr (interdiction).
Fatwā issued by Dr. Khālid Naṣr