Short answer. You do, provided you acted in good faith and indemnify the owner of the lumber for its value. The exception is where the material is worth more than the finished piece, in which case its owner may take the new thing instead, after paying you for the work.
What the law says
One who in good faith employs the material of another in whole or in part in order to make a thing of a different kind, shall appropriate the thing thus transformed as his own, indemnifying the owner of the material for its value.
Civil Code, Article 474 — Specification. Read the full provision →
The maker takes the thing and pays for the material
The default favours the person who did the work: one who in good faith employs another's material in order to make a thing of a different kind takes the transformed thing as his own, indemnifying the owner of the material for its value. Two conditions are doing the work in that sentence. The maker must have been in good faith, and what he produced must be a thing of a different kind — lumber worked into a cabinet, not lumber stacked or planed. The material's owner is not left empty-handed; he is paid what the material was worth.
When the material outweighs the workmanship
The rule reverses where the material is more precious than the transformed thing or is of more value. Then its owner has the choice: he may appropriate the new thing to himself, after first paying indemnity for the value of the work, or simply demand indemnity for the material. The comparison is between the value of the material and the value of what was made from it, and the option belongs to the owner of the material, not to the maker. Rare hardwood turned into an ordinary table is the situation the provision has in mind.
Bad faith moves everything to the other side
If bad faith intervened in the making, the owner of the material may appropriate the work to himself without paying anything to the maker, or instead demand indemnity for the material together with the damages he suffered. The maker's labour, in that case, earns nothing at all. This is why the good-faith question is the one worth settling first in any dispute of this kind: it decides not merely how much money changes hands but which party ends up holding the finished object.
The artistic exception, and what to keep
One limit runs even against an owner in the strongest position: he cannot appropriate the work in case the value of the latter, for artistic or scientific reasons, is considerably more than that of the material. Where skill has made something far exceeding the stuff it was made from, the object stays with its maker and the owner is confined to compensation. Practically, keep whatever shows where the material came from and what it cost, photographs of the finished piece, and any valuation of either — those two figures decide most of these cases.