I have had to vcarve handwriting with my router. I found the easiest way was to print a copy on paper, trace with a fine point pen (like this one) and then re-scan. After that its much darker & easier to use “trace” in software.
Don’t use a fine tip sharpie, they bleed on paper if your not moving fast enough. The above pen will also, but not as quickly.
My recommended process would be to scan and then vectorize(trace) in either adobe illustrator or a free (and very good) option is using the trace function in InkScape.
When I was going through the LightBurn tutorials there is mention of tracing inside LightBurn but personally I have not tried that yet. However, you can review the Trace Image and Weld tutorial at https://lightburnsoftware.com/pages/tutorials