Can I build and install my own lightning rods?

Most modern air points are made from aluminum. They are connected with a braided aluminum wire about the size of your thumb. You will need suitable clamps at the air points for the wire. Route the wire down from the roof and connect it to a ground rod. Be sure to connect that ground rod to your electrical, telephone, and tv antenna ground rods if any.

IIRC the 'Thompson Lightning Protection` Catalogue has good diagrams and 'how to` tips.

There are a lot of small things of which you should be aware.

Look particularly at "bodies of inductance" and "routing of down conductors".

It is probably a lot better to buy the hardware than to make it from scratch, and any outfit you buy from should offer at least some design advice if you ask for it.

Benjamin Franklin did and you can do a patent search to find his designs and copy them.