Sorry, root access is require AFAIK. For everybody who has root access and Android 4+, here a detailed description how to add it to Android's system certificate folder:
Assuming your certificate file - let's call it root.cer - looks like this:
-----BEGIN CERTIFICATE-----
MIIDgzCCAmugAw[...]
[...]
-----END CERTIFICATE-----
Obtain the name Android needs for it (".0" is appended) and store in variable $name:
name=$(openssl x509 -inform PEM -subject_hash_old -in root.cer | head -1).0
Sample output for: echo $name
00673baa.0
Create the certificate file for Android:
cat root.cer > $name
openssl x509 -inform PEM -text -in root.cer -out /dev/null >> $name
Copy certificate file to SD card:
adb push $name /sdcard
Open Android shell:
adb shell
Become root and copy certificate to Android's system certificate folder:
su
mount -o remount,rw /system
cp /sdcard/00673baa.0 /system/etc/security/cacerts/
Note: For the last command you need to replace the certificate file name!
Now reboot. Make sure that the certificate was correctly installed:
Goto Settings -> Security -> Show trusted certificates. Here in the system list you should find the name of the issuer of your self-signed certificate (which is equal to the subject). You can print it using:
openssl x509 -inform PEM -issuer -in root.cer -out /dev/null
Now you can delete all certificates (system certificates are not touched) and remove the lock screen.