Like many English words, up can be either an adverb or a preposition, and it's sometimes difficult to work out which is which, especially when it's in a phrasal verb that has a different meaning to the simple verb.
There are not so many reflexive verbs, but the rules are the same for a normal object-pronoun, so I will make some examples with non-reflexive verbs.
For adverbs, the object goes between the verb and the adverb unless it's a long or complex noun phrase. A simple pronoun is very short, so it always goes between:
Can you look it up in the dictionary?
There's no need to test the engine now: we can run it after.
The suitcase is in the attic. Can you get it down for me?
For prepositions, the object goes after the preposition:
This is a telescope. If you look up it, you can see the stars.
The cat ran after it.
That hole is pretty small. Do you think that you can get down it?
It is easy to find phrasal verbs that are only adverbal for example open it up, and phrasal verbs that are only prepositional, for example look after it, but generally even if apparently the same phrasal verb has both adverbal and prepositional usages, the meanings are usually different.
For adverbal phrasal verbs where the object is not a pronoun, it is possible to construct sentences that have the same meaning with the object in the middle or final position:
He handed over the money
He handed the money over
In Lively yourself up, the meaning of up is adverbal. In the Bob Marley song that the estimable Mr Dant provided a link to, Mr Marley clearly thinks that it has the same meaning:
Lively up yourself and don't be no drag
Bear in mind, though, that Mr Marley is not exactly a good role model for English Grammar.
There is more information about phrasal verb ordering on the British Council site, although it does not offer any guidance about when a phrasal verb can have one or two patterns.