Some threads mention the use of a HDMI dummy plug so the system believes a monitor is attached.
However, whether or not the system is headless:
Hardware accelerated transcoding requires a Plex Pass.
A GT1030 is of limited use when transcoding due to limitations put in place by Nvidia. Specifically, it does not support hardware accelerated encoding. See Video Encode and Decode GPU Support Matrix.
There are two parts to transcoding - a decode from the existing format and an encode to the new format. Since the 1030 does not support encoding, it will happen on the CPU. Your CPU might be able to support this, but you’ll have to try it to find out (see Note 1 below).
Note that streaming a 4K movie does not necessarily require transcoding. If the TV supports the audio and video formats, the movie will direct play, which requires very little CPU overhead. Your system should handle 4K direct play. As a reference point, I can direct play 4K running PMS on my NAS with a Celeron CPU.
Use the Plex Web dashboard during playback to see if the movie is transcoding (Status -> Dashboard).
Regarding the LG:
If the LG is 4K then the movie will hopefully direct play and not require transcoding.
Do not enable subtitles, as this can cause a video transcode. Enabling PGS & VOBSUB subtitles will force a video transcode. SRT subtitles will direct play, but only if the audio direct plays as well. SRT subtitles + audio transcode = video transcode.
Ideally, choose an audio stream that is supported by the TV, so it will direct play. Dolby Digital 5.1 (AC3), dts, and AAC should direct play. Direct play for TrueHD & dts-HD will depend on the specific model.
If the video does transcode, then you need to determine the cause and see if it can be avoided. Plex transcodes 4K to 1080p, which defeats the purpose of having a 4K TV & material.
Note 1: Plex transcodes 4K to 1080p. If the 1030 can perform the decode, then the encode will happen on the CPU. Plex recommends a CPU with 2000 Passmark to transcode 1080p (reference). Your CPU has a Passmark of 2600. So, if the 1030 can handle the decode, your CPU might be able to handle the encode.