Does ASL work with LiteSpeed?

Yes, ASL is supported with LiteSpeed.

Do the modsecurity rules work with Litespeed

When used with the ASL Transparent WAF (T-WAF) in front of Litespeed all rules are supported.

When using the rules directly with Litespeed, please see the official Litespeed page for what rule language features Litespeed supports:

Currently, if you do not use the T-WAF, this means Litespeed does not support the following features:

Output analysis: This means Litespeed can not inspect the output from the web server. This means rules like malware detection, malicious shell prevention, brute force protection, data loss protection and other rules that analyze the output from the web server are not supported by Litespeed, unless you use the ASL Transparent WAF (T-WAF) in front of Litespeed.
XML inspection: Litespeed has chosen to not support XML inspection, this means XML based attacks are unfortunately not protected on that platform, unless you use the ASL Transparent WAF (T-WAF) in front of Litespeed.
Multi-part Upload protection: Litspeed does not support scanning attached files content in multi-part upload. If you use the ASL Transparent WAF (T-WAF) in front of Litespeed you will be able to scan attached files in a multi-part upload.
lua: This is a language that lets us construct advanced rules. Currently they are used for advanced anti-spam protection and advanced SQLi and XSS injection protection. Therefore, these types of rules are not supported by Litespeed, unless you use the ASL Transparent WAF (T-WAF) in front of Litespeed.

Step 1) Log into ASL.

Step 2) Click on the "ASL" tab.

Step 3) Click on the "WAF Configuration" menu option.

Step 4) Click the "Add" button.

Step 5) In the "Add New TWAF Setting" window from the "Add protection for ..." drop down, select "Local Web Server"

Step 6) Select the port that litespeed runs on. Normally this is port 80.

Step 7) Check the SSL box

Enter the file system path to your SSL certificate, and SSL key in the "Path to SSL Certificate" and "Path to SSL Key file" boxes.

Step 8) Click Save

Step 1) Log into ASL.

Step 2) Click on the "Configuration" tab.

Step 3) Click on the "WAF" tab and select "WAF configuration".

Step 4) Click the "Add" button.

Step 5) Select "Local Web Server" from the "Add protection for" drop down.

Step 6) Select the port that litespeed runs on. Normally this is port 80.

Step 7) Check the SSL box

Enter the file system path to your SSL certificate, and SSL key in the "Path to SSL Certificate" and "Path to SSL Key file" boxes.

Step 8) Click Save

Note: Litespeed does not support the WAF in embedded mode.

Yes, but please see the LSWS official page for what language features Litespeed supports and does not support.