The Toledo-Lucas County Library has an index of obits that were published in the "Blade" newspapers, 1835-1969. There was no Markel listed, who died in 1954. Of course, it is possible that her name was overlooked by the library staff compiling that index.
Your best option would be to order her death cert from the State of Ohio unless you can locate a volunteer in Franklin County to view the cert for free. See http://www.odh.ohio.gov/vitalstatistics/vitalstats.aspxhttp://www.odh.ohio.gov/vitalstatistics/vitalstats.aspx for the details.
If Betty was not in the household with Louis and his second wife, Louis may have taken Betty to the Children's Home rather than trying to care for a 3 year old girl.
I checked the Lucas County marriage records and there were several Pullman females listed but no Betty or Elizabeth. Could she have used a middle name? Was Betty mentioned in Louis' obit?