"suffer" and "lack" can be used together?

Can I say:

The assets suffer from a lack of reliability.

Is suffer an admissible word in this context?

Suffer and lack can most certainly be used together. Thus, your example is correct:

The assets suffer from a lack of reliability.

Suffer goes well directly with negative nouns; some common phrases (mostly literary) are:

suffer loss • suffer want • suffer defeat • suffer depression • suffer pain • suffer shame • suffer neglect

Yes, it's fine. "Suffer" and "lack" work well together; a lack of something is possibly the most common cause of suffering.

The reason you ask this is probably that you perceive some slight overlap in meaning, which usually indicates bad style, as do most pleonasms. To suffer = to go through something negative (as in "I can tell she is suffering"); a lack = the negative situation in which there is something you do not have. And yet this collocation is fine.

As the others have noted, the verb to suffer happens to have many cast-iron idioms that contain other negative words as well. Perhaps you may feel somewhat relieved if you consider the origin of the word. It comes from Latin suffero, which means "to undergo, to bear" (its elements are sub "under" and fero "carry, bear"). "To undergo something negative" has much less of this overlap.

I believe the English verb was used with the sense "to undergo" more frequently in the past than it is now; that is probably why it sometimes feels a bit unusual in some idioms if you are not familiar with them. But any decent dictionary will still give you the sense "to undergo", even though it is now somewhat less common.