Yes, you can. The EVA lounges are between terminals C and D and it's all Airside.

After you de-board, walk towards the transfer desk. If you already have your boarding pass, bypass it and get in the security checkpoint line. After a very cursory check, go up the escalators and you'll be in the departures area.

Edit: If you can't get into the EVA lounges due to lack of invite/status, etc. On that same level is a pay lounge called "The More" which was relatively okay at roughly USD30.