Learn Croatian: Ljiljani su upravo uvenuli.

Here, 'just' refers to time, meaning 'just now' or 'a moment ago', which translates to upravo. If you meant 'only the lilies wilted' (and not the roses), you would use samo and say Samo su ljiljani uvenuli.

Is the verb uvenuli perfective or imperfective?

It is perfective, coming from the infinitive uvenuti (to wither completely). Because the wilting just finished and the flowers are now in a completed state, the perfective aspect is required. The imperfective counterpart is venuti (to be in the process of wilting).

The verb form su is an enclitic. How would the sentence look if we wanted to emphasize upravo by putting it first?

If you start the sentence with upravo, the enclitic su must still take the second grammatical position. The sentence would become Upravo su ljiljani uvenuli, which emphasizes that the wilting happened right at this very moment.

Can the verb uvenuti be used to describe things other than plants?

Yes! While its literal meaning is to wilt or wither (like flowers), it is frequently used figuratively for people or emotions. For example, you can say a person has 'withered' away from sadness or old age, or that hope has faded.