How would you translate "He's outside climbing in the tree"? There are like ten different words for climb so yeah.
I'm thinking "Je venku lezí ve stromě" or "Je venku stoupí ve stromě"? yeah I have no idea.
I second this. However, we do have the present participle (called přechodník or "transgressive"), although it is now an archaic verbal form.
Using a transgressive would yield:
Je venku, leza na strom.
Needless to say, noone speaks like this any longer. The best (real) translations have been given above:
Je venku a (právě) (=right now) leze na strom. -> if you want to insist on him being outside
Leze (venku) na strom. -> if you want to insist on him climbing up a tree (which tends to be naturally recognised as an outdoor activity ).
I'd vote for "Leze po stromě"
Leze na strom means He is just ascending the tree, from the ground up to the tree. But if he already is on the treetop, moving through the branches, that is Leze po stromě.