Are you sure of the model number? I can't find anything about a Lumix DMC-L580. There is a Lumix DMC-LS80. Make sure that you save any pictures before deleting them. Also make sure to have fresh batteries or the camera connected to AC power. If the camera runs out of power, the process will not complete.
To delete pictures from the internal memory, slide the recording/playback switch down. (The switch to the upper left of the arrow keys on the back.) This puts the camera in Play Back Mode. Use the Up/Down arrows (if needed) to select normal playback mode and press Menu/Set (in the center of the arrow keys). The delete button is the one on the right side below the arrow keys. Use the left/right buttons to select a single picture. Press delete. Press the left arrow to highlight Yes. Then press Menu/Set to confirm deleting the image. To delete multiple pictures, use the down arrow to get to Multi Delete or All Delete (instead of the left arrow). Press Menu/Set.
For All Delete, you may see an option to choose All Delete or All Delete except (star). The star indicates Favorites. If needed, pick one, press Menu/Set. Use the left arrow to select Yes and press Menu/Set again.
For Multi delete, use the left and right arrows to navigate through the stored pictures. Press the down arrow to select an image to delete. When you have marked all of the pictures that you want to delete, press Delete again. Press the up arrow to select Yes and press Menu/Set to initiate deleting these pictures. (Note: if a picture is protected, pressing the down arrow will result in On icon blinking red.)
The manual for DMC-LS80 is available from Panasonic support here: https://www.panasonic.com/au/support/manual-download/imaging/lumix-cameras/dmc-ls80.html
. The current link to the manual is https://www.panasonic.com/content/dam/Panasonic/support_manual/Digital_Still_Camera/English_02-vqt3-vqt9_other/DMC-LS80%20Operating%20Instructions.pdf
. See page 20 for the section on selecting the mode. See page 35 for deleting pictures.
I hope this helps.
(if you have a memory card in the camera, you will need to do the delete steps in two steps. Delete all (or multi) pictures from the internal memory and the memory card separately.)