Rajesh suddenly gets over his hesistation?

Raj has not yet overcome his "shyness" regarding women, not even with Penny.

• The episode starts with the gang having a meal and Raj is seen drinking out of a beer bottle before he starts talking (and judging from what's on the table he is the only one drinking alcohol)
  
  

• Before his first date with Lakshmi he is seen drinking wine:
  
  
  

• During the date at his home half-empty wine glasses can be seen on the table:
  
  

Without any real evidence, it is my experience that when I have noticed Rajesh talking to women, he always has a drink within reach. Most times in early episodes, it is in his hand suggesting easy writing, but lately the placement is more subtle. I always look for that drink to be within reach, or if not, back to the last place he sat or entered from. Sometimes it is necessary to count the beer bottles on table tops, etc. I cannot recall any time when it was not evident.

UPDATE: Here's a screen shot of their dinner date where her wine glass is in full view, but his is obscured by the salad bowl, but still evident

In an interview with the Hollywood Reporter, actor Kunal Nayyar talks about his character's development with regards to women, explaining that his newfound confidence is a result of his having spent the night with Penny at the end of season 4:

“What happens that night really gives him this level of confidence,” Nayyar says. “Whether that works in his favor or doesn’t, it does give him some self belief.” While Nayyar was mum about whether or not Raj would romantically pursue his best friend’s ex-girlfriend, he hopes Raj’s newfound confidence is just a small step forward for the character who at the end of Season 4 was still only able to speak to women with the assistance of alcohol.

“Do I hope that Raj becomes this womanizing player who can talk to women all the time? No, I hope that he continues to grow,” Nayyar says. “I really think if you take away a character’s obstacles then there’s no comedy. Comedy is really based on overcoming obstacles and if you take away that obstacle, my fear is that [Raj] would lose his funny.”

In Season 4, episode 14, eight minutes into the show Howard and Bernadette come to tell Rajesh that Howard has been offered a fellowship at Weizmann Institute. Raj is sitting at a table in the university cafeteria. He is holding a green aluminium can. Since to my knowledge, none of the characters have ever drunk alcohol in the cafeteria then the can must be soda. In this scene he is having an open conversation. The can has a lime slice and the letters 'nist' visible. Although this scene is Rajesh's fantasy; Howard wants Raj to take care of Bernadette's sexual needs while he is away, it indicates a change in his, Raj's, character.