You should apply for the renewal 90-120 days before it expires. If you apply more than 120 days in advance, they'll reject it for applying too soon; if you apply with less than 90 days remaining on the existing one, it might not get renewed before it expires, as the mandated time frame for processing is 90 days.
Still, although the EAD belongs to you and you can apply to renew it without your employer's involvement, you may be able to get your employer to pay for it. Most employers will pay for the EAD renewal if they are the original sponsoring employer for the GC. However, if you filed the I-485 after the Summer 2007 fee changeover, EAD and AP renewals are free* so there would be no need to ask for the employer's assistance.
*built into the I-485 $1010 fee