LastPass has indeed been hacked into a couple of times, but I haven't heard of any account takeovers as a result. With regard to the incident you mention, the severity depends on how strongly those passwords were hashed.
You could argue that LastPass gets hacked because it's got the highest profile. (That's Microsoft's argument, anyway.) Or you could choose to avoid LastPass because it's had to settle two different complaints with the FTC over false advertising, or because it got bought by LogMeIn. But none of those facts affect its usability and value as a service.
As for the password-reset questions such as "What was your mother's maiden name," getting around that is easy. You can, and should, lie, especially when the answer is something that can be easily discovered. So tell them your mother's maiden name was Minnie Mouse or Olive Oyl, and just remember that.