Although "intentar", as a transitive verb, usually takes a direct object, it does not always need one.
It is perfectly correct to say, in the proper context:
We can find it accompanied by some structure to reinforce the idea that, no matter what the result may be, you will make a try:
Al menos intento // No sé si podré pero intento // Por más que intento no lo consigo.
This is in line with the grammar of transitive verbs which, according to the RAE, can do without the direct object without ceasing to be transitive. Item 34.5.1a of RAE's grammar says:
Estos verbos [con complemento directo omitido] no dejan de ser transitivos en tales contextos, ni pasan a adquirir en ellos un nuevo significado. De hecho, es posible remitir al elemento que queda sobrentendido.
The element that is understood in "Intento" is whatever the person is trying his/her hand at. It is worth mentioning that "Lo intento" or "Intento" (with "intentar" being transitive in both cases) is equivalent in meaning to: "Trato", which is intransitive.
I find this use of "intentar" without an object similar to that of "buscar" which, even if usually accompanied by an object, does not always require one. Noone can deny that this sentence from the Bible is correct: El que busca encuentra. By analogy, we can very well say: El que intenta consigue. Although the thing tried or sought is implicit, it need not be expressly stated.
The case of:
is different. "Lo siento" is similar to "Lo lamento" (though the latter is quite stronger). Though unusual, "Siento" alone can be used to mean "I have feelings", in a context like the following:
Pienso, siento, estoy vivo. (I think, I feel/have feelings, I'm alive.)
To mean "I'm sorry", "lo" is required, and the pronoun will refer to the situation the speaker is sorry for.
Note: Here I've found a couple of interesting examples illustrating the use of "intentar" without an object:
Él trata de hacerlo, intenta, pero no lo logra. (Source) (Notice that while "hacer" and "lograr" do require a direct object, "intentar" does not.)
Edipo intenta pero falla. (Source)