Hi Cynthia, this isn't possible with Asset Essentials and Lightroom.
Asset Essentials doesn't allow for custom integrations. For that you would need AEM Assets Enterprise. Lightroom isn't an out-of-the-box connection to Asset Essentials, so you'd either need the Adobe product team to build an out-of-the-box connection OR you'd need to upgrade to AEM Assets Enterprise and build a custom integration.
Asset Link (as suggested below) doesn't currently support Lightroom and I don't believe it's on the roadmap. Asset Link is also only supported by AEM Assets Enterprise.
That's the bad news. I think the good news is that you probably have ways of accomplishing a similar set of functions if you aren't too attached to a specific way of doing things. If you use Bridge or CaptureOne (and I presume Lightroom, although I haven't seen it done) to tag assets before ingesting them to Assets Essentials, you can have that pre-DAM metadata flow through to Asset Essentials. This works best for Dublin Core fields like title, description, or keywords OR IPTC fields like photographer. But if you pay attention to the DAM metadata field name AND the location of the tag field, you could work with almost any field (at least in Bridge--Lightroom is less flexible). Tags might be a bit tricky--I believe that structure would require some pretty specific syntax to be entered in Lightroom or Bridge.
Hope this helps,
Beau