wp_get_attachment_caption to pull Image Caption or alt

You can directly get an attachment’s meta data if you have it’s ID. The alt data for an attachment is stored in _wp_attachment_image_alt.

So, you can use:

$alt = get_post_meta( $attachment->ID, '_wp_attachment_image_alt', true);

To get the caption of an image, you can use wp_get_attachment_metadata().

$metadata = wp_get_attachment_metadata( $id );
$caption = $metadata['image_meta']['caption'];

EDIT

Based on the code in your comment, this is the full shortcode’s code:

function simplisto_the_image($atts) {
    $atts = shortcode_atts(
        array( 
            'to' => 'http://example.com/image.jpg' 
        ), 
        $atts
    );
    $caption = '';
    // Get the attachment's ID from its URL, if the URL is valid
    $url = filter_var( $atts['to'], FILTER_SANITIZE_URL);
    if( filter_var( $url, FILTER_VALIDATE_URL) ) {
        $attachment_id = attachment_url_to_postid( $url );
        // Get the attachment's alt, if its a valid ID
        if( $attachment_id ){
            $caption = wp_get_attachment_caption( $attachment_id );
        }
    }

    $output="<div class="lazyimg">"; 
    $output .= '<img class="lazyimg-popup" src="'.$atts['to'].'" alt="' .$caption. '" width="100%" height="auto">'; 
    $output .= '<i class="fa fa-expand" aria-hidden="true"></i>'; 
    $output .= '</div>'; 
    return $output; 
}
add_shortcode('simage', 'simplisto_the_image');

The shortcode will accept an image URL and fetch it’s metadata, if it’s valid.