Can I apply for my Visa before my I94 expiry date

Hi ,

My L1B Visa has expired in Nov 22 2012 and I have a I94 till 15 Apr 2013.

Can I apply for my Visa transfer to L1A in March 2013 (which is a month before I94 expiry date)? Is that a Lega scenario considering my L1B Visa has already expired ?

Also, My company is willing to file an H1B in 2014 quota. Can I file it in April?