Learn Turkish: Yalanı sadece ona söyletiyorlar. - They are making only him tell the lie.

This is the core rule of causative verbs! The base verb söylemek (to tell/say) is transitive, meaning it already takes a direct object (yalanı). Since the direct object slot is already filled, the person who is made to do the action (the causee) is bumped to the dative case (ona). If the base verb were intransitive (like crying or sleeping), the causee would take the accusative case instead.

How exactly is the causative suffix formed on söyletiyorlar?

The base verb stem is söyle- (to say/tell). Because this stem ends in a vowel, it takes the causative suffix -t, becoming söylet- (to make someone say/tell). After that, it simply gets the standard present continuous ending -iyor and the plural subject marker -lar.

Why does yalan (lie) have the -ı suffix?

The -ı is the accusative case marker, showing that yalanı is a specific direct object. They aren't making him tell just any lie; they are making him tell the lie.

Why is sadece ona placed right before the verb?