La parte arrendataria le comunica a la parte arrendadora que perdería la fianza.
In the sentence the owner (la parte arrendataria) is telling the tenant (la parte arrendadora) that the tenant will loose the deposit.
"Le" seems to refer to the la parte arrendadora.
Can the "le" be omitted?
Duplicating the indirect object or the direct object is pretty common in Spanish, as you can see here.
In relation with your sentence you can also find this detailed explanation:
Se ha observado, no obstante, que la ausencia de doblado en estas construcciones es más propia de la lengua escrita que de la oral. En el registro conversacional de muchos países hispanohablantes se siente poco natural la ausencia de doblado en secuencias como Di la noticia a mi marido (o a mi esposo, según los países) en lugar de Le di la noticia a mi marido, ya que la primera variante se asocia con un nivel de lengua más formal.
That more or less can be translated as
It has been observed that the absence of the duplicate in these constructions is more characteristic in writing that in speaking. [...] in a lot of Spanish-speaking countries they feel less natural the absence of the duplicate in sequences like Di la noticia a mi marido instead of Le di la noticia a mi marido because the first variant is associated with a more formal level of speaking
So applying that to your sentence, the answer is yes, it can be omitted, but such variant is considered more formal. Talking about contracts and official communications such level is usual.
La parte arrendataria comunica a la parte arrendadora que perdería la fianza.
In any case, as noted by Lambie, the sentence seems uncompleted. It's missing the condition that describes in which cases the deposit will be lost.
On the other hand, as PeterM commented, "parte arrendataria" means tenant and "parte arrendadora" means owner. Usually it's the owner the one that communicates cases in which the deposit will not be returned. So it should be
La parte arrendadora comunica a la parte arrendataria que perdería la fianza en los siguientes supuestos: ... [listado de condiciones]
Some conditions that can result in losing the deposit (in Spanish):
While I am not a native speaker, in my opinion the "le" cannot be omitted.
Within this sentence, the "La parte arrendataria" is announcing/stating (comunicar) that " .. perdería la fianza.". So that person is performing the action.
However, the action is not being performed in a vacuum. Instead it is being directed at "la parte arrendadora", who are the recipient of the action (announcing/stating). As such, you need a "le" to indicate the recipient of the action. And because the "la parte arrendadora" hasn't been defined before this sentence in some manner, you still need to specify who was actually receiving the action.
(If the previous sentence had mentioned something about the two parties meeting, then you could drop the full explanation of who both parties are from your example sentence sentence.)
This form is exactly the same as for other verbs like "dar" for example. So you could say:
La parte arrendataria le da una carta a la parte arrendadora
The action is the owner giving a letter, but the recipient is the tenant.
