Is GPL-2.0-only compatible with LGPL-3.0?
No.
LGPLv3 cannot downgrade to GPLv2-only; needs GPLv3.
General guidance, not legal advice.
Obligations when redistributing as open source
No obligations checklist — this combination cannot be distributed as a single work.
Other distribution models
The verdict is the same under every distribution model; the obligations differ. Check this pair in the tool to switch models.