You say "automation", so you want numbers? It is possible to build an LFO in the Logic Environment (with adjustable waveform). Here is a screenshot but I don't have the original file anymore: LFO for automation
If you want an audio LFO, you may try the Plogue Bidule plugin right in Logic. There is a basic oscillator for frequencies 0-20 kHz and several waveforms. I don't know how Bidule can convert the audio output of the oscillator to MIDI but I think it is possible.
You can of course build all kinds of oscillators in applications like Max/MSP and send them to Logic.