Found it!
The working code is as follows:
@foreach ($alert->faults as $key => $value)
Graph for the last hour:<br>
<img src="data:image/png;base64,{{base64_encode(file_get_contents('https://monitor.local/graph.php/device=' . $value['device_id'] . '/type=device_processor/width=800/height=300/lazy_w=552/from=end-1h'))}}" alt=""><br>
@endforeach
I had to to make sure it fiddled in the code : @foreach ($alert->faults as $key => $value) and had to make sure the variable for the device started with a SPACE and DOT and SPACE; the same for after the variable and all of this between two quotation marks. That’s it!
Now only if MS Webmail could show the image; only my iOS device and Outlook 2016 can show it (while this is enough for now); it would also be a nice to have to let MS Webmail show the image. Anybody ideas on this ?