I have lilo installed on the MBR of hda, which can boot Windose on hda, and Linux (Mandrake 9.2) on hdb.
If hda failed, I would have no access to Linux, except for my GRUB floppy.
My question is
would it cause any problem to install GRUB to the MBR of hdb, just in case my hda decided to retire?

That would be fine. Do it once, then change the boot/lilo configuration back again to how it was originally. Some computers allow you to press a key such as ESC or F3 before the booting process to select (one time) which device to boot from. You could check it this way. Otherwise , you could could make the changes in BIOS so that the second drive boot instead. If using grub, it boots OK, then you can change it back.

You don't need to use grub on the second drive just because LILO is on the first. You could change the boot= entry so that the MBR on /dev/hdb is changed, run /sbin/lilo, change lilo.conf back again and rerun /sbin/lilo.

Another option would be to add an entry to lilo that chainloads the /dev/hdb boot loader.

Thanks,
That is a good idea on running lilo twice with the different conf.