To replace a lost motor vehicle log book in Kenya, you need the following documents:

Application for XI (Available here)

Copy of ID/Certificate of incorporation/ Business Registration Certificate

A fee of Ksh. 500 for filled up  and Kshs.2,500 for defaced or lost Logbook

A police abstract in case of lost logbooks (available here)

Submit these to the nearest KRA office (See a list of all KRA offices countrywide here)