No, cancelled titles are not available in myLTSA Explorer. You can only order registered titles, State of Title Certificates, and plan images.
Registry agents and other professionals can electronically request cancelled titles on your behalf. See Hire a Professional to Assist You for more information.
Alternatively if you are a business or professional customer, you may wish to consider registering for a myLTSA Enterprise account for access to the full suite of the LTSA's Electronic Services.