Leaves closeup.

Trunk closeup.

It looks like lemon guava, (Psidium littorale.) In favorable conditions it will produce fruit.

Google doesn't give many hits for the lemon variety but the leaves do look similar. Although I have never seen any kind of blooms on this plant let alone fruit. I'm thinking of taking cutting and trying to root it. Do guavas root easily?

I have one of my own and the blooms are really easy to miss. Mine blooms in late spring and the small white flowers usually fall off.

The coppery-red growth up top and the smooth, peeling bark are tell-tale characteristics of Psidium littorale. It's fairly common, you should be able to find these at nearly all big-box nurseries in Southern California if your cuttings don't root.