Recently I downloaded latest kde neon amd64.iso. I don't know how it's corrupt. But can I install amd64 software on i686 architecture ?
You CAN run 64bit (=x86_64 in redhat and relatives, =amd64 in debian relatives) or 32bit (i386-i686) software (code, kernel, OS) on 64bit (AMD64,EM64T) enabled x86 compatible hardware (CPU).
Check support with HW vendor. Generally speaking AMD Athlon64 and newer, Intel Xeon Nocona/Pentium Prescott and later are 64bit CPUs.
More in https://en.wikipedia.org/wiki/X86
Note: Intel IA-64 Itanium are (usually) not 32bit enabled.
You CAN NOT run 64bit software on 32bit hardware unless you use full HW virtualization (like qemu - not KVM).
You may have 32bit OS running on 64bit HW while running lscpu. Your reported architecture (SW) is then i686 but you can still boot 64bit ISO if it's not corrupted. You may check MD5/SHA checksum to check for corruption.