Dave Connell's side dominated the game in Alytus from the opening whistle, but it took over 30-minutes for the side to beat Lithuanian goalkeeper Vilte Jurgaityte.
Payne opened the scoring on 31-minutes, which opened the floodgates for the Irish attack. Alannah McEvoy and Isibeal Atkinson also found the back of the net before the break.
Despite the 3-0 lead, Ireland lacked any complacency at the start of the second-half as Tiegan Ruddy scored inside 60-seconds. Payne scored once more four-minutes later to give Ireland a 5-0 lead.
With the three points wrapped up, Connell made four substitutes and was rewarded with both Chloe Singleton and Carla McManus coming off the bench to score past substitute goalkeeper Dominyka Vaiginyte.
Speaking after the game, Connell was thrilled with his side's performance against the Qualifying Round hosts.
"The experience from previous years helped is today. It was a professional, ruthless performance. We took our chances. The squad was excellent today.
"We spoke at half-time about not being complacent, and I was delighted to see Chloe and Carla come off the bench and score. The depth of the squad is brilliant.
"To score seven goals and not concede any was pleasing."
Connell's side will hope to make it two wins from two on Friday. They play Faroe Islands in Marijampole. Kick-off is at 3pm (1pm Irish time).
Republic of Ireland: Erica Turner; Rachel Baynes, Sadhbh Doyle, Roisin McGovern, Lucia Lobato (Doireann Fahey 66); Megan Mackey (capt), Tiegan Ruddy (Sinead Donovan 78), Ciara Fowler (Chloe Singleton 63), Heather Payne (Carla McManus 63), Isibeal Atkinson (Louise Masterson 63); Alannah McEvoy
Lithuania: Vilte Jurgaityte (Dominyka Vaiginytė 50); Gintare Blazyte, Gabija Gedgaudaite (capt), Urte Smigelskaite, Agneta Patilskyte; Liucija Vaitukaityte, Guste Klimasauskaite (Kamile Pranulyte 50), Simona Bagaviciute (Gabrielė Vitovskyte 64 (Guostė Jonikaitė 81)); Gabriele Ragauskaite (Viktorija Ciapaite 50), Erika Deventinaite; Loreta Rogaciova
Referee: Ruzanna Petrosyan (ARM)