I've been trying to get more used to dealing with two verb sentences, but I just came around the doubt if you can change those verbs around. Like, is "er baut sich ein Haus leisten" the same as or sililar to "er lässt sich ein Haus bauen". If not why? And/or which one sounds better.
As already mentioned in the comments, leisten and lassen are two different words. leisten means to afford sth, lassen means to get sth done (in this case).
Your first sentence "er baut sich ein Haus leisten" doesn't make sense. The only way I can think of that this sentence could make sense is to say "er kann es sich leisten, ein Haus zu bauen" or "er leistet es sich, ein Haus zu bauen" (meaning that he can afford to build a house).
In the second sentence, "er lässt sich ein Haus bauen" (he gets a house built), the ordering of the two verbs is important. You can't change them into er baut sich ein Haus lassen, that would be wrong.
In general, I think, the order of the verbs is important and cannot be changed. Other examples would be "Sie geht schwimmen", "Sie lassen sich feiern", "Es schneit, nachdem es lange geregnet hat". Note that in the last sentence, you could turn the two half-sentences around, but that's only, because these are two sentences that are concatenated.
I'd say that in most cases, if you have only one sentence, where the verbs belong together, you can not easily turn them around.
The term "two-verb sentence" is somewhat unfortunate. What we have here is a finite auxiliary verb and an infinite full verb. Actually it should rather be regarded as a single verb consisting of two parts. The position of these cannot be changed freely, and in particular they cannot be exhanged.
English has similar constructs. What you are trying to do is like rewording "He is building a house" as "He builds being a house" which obviously does not make any sense at all.