In short: no, it's not possible.
Longer answer -- it depends on what you mean by "lock the screen". When people hear that phrase, they typically think it means to lock the device such that the user cannot do anything else -- the security screen that prevents them from going far when they turn the device on (until they satisfy the screen with a pin, pattern, facial recognition, etc).
In your question you mention wake locks and the power manager -- which is not significant in the security lock screen; this is significant if what you really meant was "lock the screen on", or "don't allow the screen to auto-turn off" while this activity is active. If that's what your intention is, then yes, you can do that. From How to get an Android WakeLock to work?, you'll need a permission in your manifest:
<uses-permission android:name="android.permission.WAKE_LOCK" />
and you'll need code resembling the following to enable your wake lock:
private PowerManager.WakeLock wl;
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.main);
PowerManager pm = (PowerManager) getSystemService(Context.POWER_SERVICE);
wl = pm.newWakeLock(PowerManager.FULL_WAKE_LOCK, "DoNjfdhotDimScreen");
}//End of onCreate
@Override
protected void onPause() {
super.onPause();
wl.release();
}//End of onPause
@Override
protected void onResume() {
super.onResume();
wl.acquire();
}//End of onResume
while the following would disable it when you're ready:
w1.release()