él tuvo la intención de ......
Intentar is transitive, yes. But here you made it reflexive, saying "He tried himself."
Neither "Él intentó" nor "He tried" are actually complete sentences, although both can be attested to becoming more popular recently as a short means to say "Well, he didn't succeed, but at least he tried (the task)". For a more grammatically sound sentence, I'd go for "Él lo intentó" - "He tried it."
There was an example in the duo lessons: "Ella no me lo permitió". According to discussion, here lo is added because permitir is transitive verb so it will need direct complement of some sort. You can see the discussion here: https://www.duolingo.com/comment/12800764 Also, I checked following website where it gives example, like the first one here: http://www.spanishdict.com/translate/permitir I take your larger point though that this is not a complete sentence but used colloquially in english. So perhaps what I wrote means "He tried (it/those things)"?
Yes, there's a similar issue with permitir, it doesn't work well without a direct object. Even less than intentar, I guess. :)
I think the main issue with that discussion is, though, that in English "She didn't allow me it." sounds awkward, but if you leave out the indirect object, it's much better: "She didn't allow it."
The example you linked has a small problem: it's a passive sentence. It's not the dogs that allow something (or disallow in this case), but they're the thing that is disallowed. Passive voice is expressed in Spanish with se and a 3rd-person verb. Or I guess you can say it reflexive: "Dogs do not allow themselves".
So the sentence you suggested, "Él se intentó" could either be the reflexive "He tried himself" or the passive "He was getting tried". "Trying" a person doesn't make a lot of sense in Spanish.
So, as with "Ella no me lo permitió", I'd suggest adding a general lo as the object. "He tried it."
I see. so instead of "se", add a "la/lo" as direct object pronoun instead of object itself? Also I did not know that "se" was used as a passive voice. Clearly dogs were the object of the sentence so that was passive voice. Thanks for that information. Also if the object does not prefer gender then do we use "lo" over "la" by default in spanish?
Yes, lo can be used as a general, abstract or non-defined object. La is only used if the object is defined (and it's feminine, of course).
Se has a couple of different uses in Spanish, but mostly it's used as a reflexive object pronoun, i.e. the object is the same as the (3rd-person) subject. Ella se lava. - She washes herself. Se can also function as a generalised "you" or "one": Esto no se hace. - You don't do this./One doesn't do this. (Or passively expressed "This is not done.")