Thanks for reaching out. We are sorry about the crash with Lightroom & Photoshop. I'll need more information to help you with this.
Could you please share the version of Lightroom or Lightroom Classic you are working on & the system info of Photoshop from Help > System info > Copy & paste into a text document > upload to Creative Cloud files (https://assets.adobe.com/files) and share with us? Do you see an error screen or pop up before the applications crash?
Does this crash occur only when using Lightroom & Adobe Photoshop together?
If you are working on Lightroom Classic, where is the catalog stored? Is it on the internal drive or an external drive?
Have you tried any troubleshooting steps?
To begin with Lightroom & Lightroom Classic, please go to Edit > Preferences > Performance > Use Graphics Processor > Set it to Off if it is on Custom or Auto. If this shows you any differences in performance, please check this article to troubleshoot further: https://helpx.adobe.com/lightroom-classic/kb/troubleshoot-gpu.html
Similarly, please go to Photoshop > Preferences > Performance > Use Graphics Processor > Uncheck it and restart Photoshop. You can also optimize Camera Raw, which handles Raw images in Photoshop, by going to Photoshop > Preferences > Camera Raw > Performance > Uncheck Graphics processor and increasing the cache sizes.
Please check this series of suggestions related to software optimization and in-app changes you can do to optimize Photoshop's performance in this article, and please give this a detailed read-through: https://helpx.adobe.com/photoshop/kb/optimize-photoshop-cc-performance.html
Let us know if this helps.