Hi, sorry for not replying sooner
I'm not sure what sound editing program you're using, but I believe doing this can be done in pretty much the same way in most programs -- just in case, the steps below apply to the Easy Voice Recorder (comes free with LR), Adobe Audition, and Audacity:
- Open your audio file in your editing program
- Highlight the silent (straight line) part of the sound's waveform
- Click DELETE to cut that part off
You may notice that after saving your work and opening it again, a bit of silence was appended to the beginning/end of your file. Most editing programs do add an extra silence at the beginning and end of files by default, so in the end you may not be able to do this perfectly.
I hope this helps, though!