You can use a pubsub emitter/dispatcher pattern. I call this LWC a messageBroker. You can find a working example of LWC and Aura interoperability in my repo here
Basically, to have uni (even bi-directional) data move from LWC to aura, right now the best technique is to place an Aura wrapper somewhere on your flexipage.
With a standardized LWC pub-sub channel messageBroker (or whatever you want), the LWC parts are as follows:
lwcRequestor.js
fireEvent(this.pageRef, 'messageBroker', payload});
// payload.data
// payload.recordId, etc
messageBroker.js
import { LightningElement, wire } from 'lwc';
import { CurrentPageReference } from 'lightning/navigation';
import { registerListener, unregisterAllListeners } from 'c/pubsub';
export default class MessageBroker extends LightningElement {
@wire(CurrentPageReference) pageRef;
connectedCallback() {
registerListener('messageBroker', this.messageBrokerEmitter, this);
}
disconnectedCallback() {
unregisterAllListeners(this);
}
messageBrokerEmitter(payload) {
// Just pass this on through to the parent enclosing aura component
this.dispatchEvent(new CustomEvent('message', { detail: { payload } }));
}
}
Then the aura component below placed on your flexipage. This is important because of the current limitations of the lwc-recipe pubsub component requires @wire pageRef. (Though you can strip that check out if you want, and swap for say - a recordId).
This aura wrapper is as such:
MessageBrokerAuraHandler.cmp
<aura:component implements="flexipage:availableForAllPageTypes">
<c:messageBroker onmessage="{! c.handleMessageBroker }"></c:messageBroker>
</aura:component>
Then you're freely able to handle the LWC's payload in your aura component via c.handleMessageBroker.
Best Answer
Yes you should be able to do this by wrapping up the LWC base component in a custom LWC Component. You can use custom LWC component in an Aura Component. Use this link to understand how to use custom LWC in aura component: https://developer.salesforce.com/docs/component-library/documentation/lwc/lwc.interop_aura_composition This way you should be able to use benifit of LWC with existing AURA Component.