In photosynthesis, the energy from the sun is used to turn carbon dioxide (CO₂) and water into sugar. Oxygen is a waste product. Plants then put the sugars together to make other molecules. One is starch. This is a way for plants to store energy for later. Potatoes and grains are full of starch. Another is cellulose, which makes plants tough. Another is wood.

The wood that becomes lumber was made through photosynthesis and other processes. Those other processes use energy that was captured in photosynthesis. The tree breaks down some of the sugar to provide energy to do the work of putting the smaller molecules together to make the wood.

So most of what you see as lumber used to be the gas carbon dioxide.

Why is photosynthesis so important to us animals?

That is an interesting question and involves several steps to go from photosynthesis to lumber production. Let's start in reverse with photosynthesis. This is the photo-chemical (requires light energy) reaction by which plants capture sunlight and convert it into chemical energy (sugars). It occurs mainly in leaves but can also occur in the bark/stems of some plants. Photosynthetic regions of a plant tend to be green as they absorb all other wavelengths of light except for green. The sugars that are produced are then used for everything imaginable in a plant; from moving water to absorbing nutrients to growth to the production of wood. Woody plants use molecules called lignin and cellulose to create thick, dense hard structures that provide support for the plant to grow against the pull of gravity. This is the wood that industry calls lumber. So overall, photosynthesis converts sunlight into sugars which are used to fuel the construction of wood (lumber).

Lumber is wood. Wood is from the stems of trees, which grew that wood using energy from the sun collected via photosynthesis. Thus the rate of growth and production of lumber depends on the rate of photosynthesis.