Hi Jaw,
APs will work with static ip address but to give static ip address either your APs should join controller and then you can specify ip address from controller OR you can have to take your APs in rommon to configure them with static ip address which is not a very feasible and easy solution.
So to make your AP join first it should get an ip address from DHCP server. Also if your APs are in different subnet then controller then you need to pass option 43 or dns information to the AP about your controller management ip address which is only possible through DHCP server.
And that is the reason we state that when operating in L3 lwapp mode APs must get an ip address through DHCP.
Can you confirm how did you assigned the statis ip address to APs?
Regards,
Ankur