Well, I think there
is a way to express third type conditional in Arabic. As for the second type, maybe not all its aspects can be expressed as exactly as in English.
In Arabic, لو has many functions. One of them is expressing what is called in English "impossible conditions",
whether in the present or the past.
(Information and examples in English are based on this
page and this
page.)
Third conditional is used "to talk about 'impossible' conditions, impossible because they are in the past and we cannot change what has happened".
لو+ماض... لَـ in Arabic can do the job. It can be used to express impossibility of something for being in the past. For example:
If I had seen him at the meeting, I would have asked him can be rendered: لو رأيتُه في الاجتماع لَسألتُه
If she'd invited me, I'd have gone to her party can be rendered: لو دعتني لَذهبتُ إلى حفلتها
As for the second conditional, when it's used to express "impossible" situations which are not in the past, you can also use لو+كان+اسم كان+مضارع... لَـ in Arabic. For example:
If I had millions of dollars, I'd give a lot to charity. This can be rendered: لو كنت أملك ملايين الدولارات لَتبرّعت بمال كثير للجمعيات الخيرية.
If I lived in Japan, I'd have sushi every day: لو كنت أعيش في اليابان لَأكلت السوشي كل يوم.
This لو can also be used in "if I/you were" constructions. For example:
If I was/were the President, I'd reduce taxes. This can be rendered: لو كنت الرئيس لَخفضت الضرائب.
Note that "if I were you" is rendered in Arabic: لو كنت مكانك (literally, if I were in your place). For example:
If I were you, I'd look for a new place to live. This can be rendered: لو كنت مكانك لَبحثت عن بيت جديد أعيش فيه.
Now, it seems that the main difficulty lies in the following. The webpage explains:
Note that the choice between the first and the second conditional is often a question of the speaker's attitude rather than of facts.
My personal opinion (I might be wrong and I wish other members of the forum would correct me) is that this "speaker's attitude" cannot be easily conveyed in Arabic. The reference gives some examples for comparison, where "Otto thinks these things are possible, Peter doesn't". Here's one of them:
Otto – If I get promoted, I'll throw a big party.
Peter – If I got promoted, I'd throw a big party.
They're both usually rendered in Arabic: إذا حصلتُ على ترقية فسأقيم حفلة كبيرة. I don't think you can easily convey this "attitude" in Arabic, but it could be understood from the context. Of course, you may add something like: إذا حصلت على ترقية، وهذا مستبعد جداً (وهذا شبه مستحيل)، فسأقيم حفلة كبيرة... but only if you had to.
Note: if the construction expresses strong wishing, you can use لو+مضارع...فـ:
لو أحصل على ترقية فسأقيم حفلة كبيرة.