I am trying to understand what Lastpass can and cannot protect me from. For example, I have read that if the Lastpass servers get cracked, my data is still safe. But what if MY computer gets cracked? What if I pick up malware? Does that event compromise all the data that is in my vault?
LastPass unfortunately can't do everything for you, so this is a threat that is your job to mitigate. Besides safe browsing habits and using antivirus clients, there are account security features you can use to reasonably minimize the effect of malware or compromised credentials.