The 24-year-old joined from Racing 92 in the summer, with Adam Hastings firmly established at fly-half. After limited chances, Lancaster impressed in Champions Cup matches against Clermont and Saracens and will start against Munster tonight.
"Adam has been playing great and you can see that by him getting called up for Scotland and by the way the team's gone," Lancaster told Scotland Rugby News. "Obviously as a competitive bloke and as a 10, you want to be starting.
"I'd be lying to say it hasn't been frustrating at times but again you've got to put the team first and then it makes it amplify that when you do get an opportunity you've got to take it otherwise that's an opportunity missed. I definitely had to be patient but again that's why I'm probably happier. I feel like I'm contributing now."
With Hastings set to depart for Montpellier this summer, Lancaster is ready to embrace a bigger role.
He added: "I think it's great for Adam. He's got a new challenge at Montpellier, one which I think he'll be really excited for. I'm sure he'll work as hard for the team's success this year and obviously to push his game and push forward. For me it's a great opportunity.
"I think I've earned a bit of trust now with the last couple of games and I think as a player coming into a new environment you've got to earn the trust, earn the respect of the coaches, the players and people around you. So hopefully I've done that and hopefully they can trust me moving forward. Hopefully next year I'm first choice playing a week out and cracking on."
Despite a depleted backline against Munster, Lancaster has relished playing alongside Glasgow's attacking talent.
"I wouldn't obviously say it's easy but I feel like the team operates best when you give them a clean ball and almost let them shine," said Lancaster. "We've got two British and Irish Lions. Huw Jones has been back and played great.
"Obviously Stafford (McDowall) was great before Huw was back, Jamie and Kyle are amazing. They are two unbelievable players. Jamie obviously plays nine and wing. He's unreal so it's just my job to give them the ball and let them shine. You obviously played against Glasgow before you joined."