The installer checks whether /usr/lib/crt1.o exists. This file does not exist until the command line tools are explicitly installed (this is separate from "clang" etc being available on the command line). Have you also checked the updates section of the App Store application? Maybe you upgraded Xcode, but not the command line tools (you can only upgrade them via the App Store application after initially installing them via xcode-select).
I'm also having trouble installing Lazarus 1.6 on El Capitan 10.11.5. Xcode 8.1 is installed, as is:Command_Line_Tools_OS_X_10.11_for_Xcode_7.3.1Lazarus will compile a basic empty application, but when running it both the green "Run" and red "Stop" buttons remain on but do not work, the application does not appear, and I have to force quit Lazarus.
gdb was also installed and codesigned. It turns out I had to force a new codesign using the -f option. It works now.