Villafáñez made his professional debut in the Primera B Nacional with his hometown club Comisión de Actividades Infantiles, when he was 16 years old. In total he played 57 games with the club, scoring 12 goals. In 2010, Independiente acquired the player on a one-year loan deal. He debuted in the Argentine Primera División on a 0–1 defeat to Tigre for the 2010 Apertura, despite the game being played in February 2011. On 2 May 2011, Villafáñez scored his first goal with Independiente, in a 1–1 draw with Boca Juniors. In summer 2013, the hitch that had a contract until June 2014 and would not be taken into account by Miguel Angel Brindisi was asked by Antonio Mohamed after his arrival in Huracán F.C. and eventually would be signing with the "Globe". After several days of negotiation and obstacles, it was finally decided that Villafáñez would go on loan to Huracán F.C. for the 2013–14 season. On 1 August 2014, Villafáñez signed a two-year contract with Greek Super League side Panetolikos on loan from Independiente, along with his former Independiente teammates Fernando Godoy and Nicolás Martinez. In December 2015, Villafáñez was linked with a move to AEK Athens. On 24 January 2016, he scored with a close-range effort at the beginning of a match against Veria which Panetolikos won 1–0 and scooped its first away victory since August 2015.
Panathinaikos
On 27 January 2016, Panathinaikos bought the Villafáñez's playing rights from Independiente, so from the summer of 2016, he would have belonged to the "Greens". Panetolikos, however, wanted to make a profit form the player's transfer and gave him to Panathinaikos from 1 February. On 6 March 2016, he scored his first goal with the club in a 2–0 home win against Atromitos. On 28 October 2017, thanks to a close-range effort by the Argentinian attacking midfielder, Panathinaikos won 1–0 at Super League derby clash against champions Olympiacos. On 7 January 2018, Marinos Ouzounidis’ team, which had last tasted victory in the Super League back on 28 October with a 1–0 derby win over Olympiacos, finally stopped the rot in the first game of 2018 thanks to a pair of penalties from Villafáñez in a 2–0 win home game against Platanias. On 14 January 2018, with Panathinaikos in financial difficulties, French website "Foot Mercato" reported Villafáñez had been offered to three Ligue 1 clubs, namely Nantes, Saint-Étienne and Toulouse for the January transfer window on a loan basis till the end of the season with a purchase option in the range of €2 million for the summer of 2018. Villafáñez left the club having 73 appearances in all competitions.
On 23 January 2018, Turkish club Alanyaspor initially offered an €800,000 transfer fee to Panathinaikos for Villafáñez. The transfer offer involved two Greek internationals, Giorgos Tzavellas and Giannis Maniatis. According to various sources, the transfer could be set in the range of €1.1 million, with Villafáñez agreeing to a 2.5-year contract, with annual earnings levelled to €800,000 per year. After three days of negotiations, Panathinaikos agreed with Alanyaspor for a total transfer amount of €1.2 million. The financial struggling Greens will receive a net amount of €900,000, as Villafáñez ex-club Panetolikos retained a 10% resale rate, while from the total transfer amount Panathinaikos will cover his debt both to the player's rights from Independiente and his annual delayed salary. On 27 January 2018, two days after his arrival, he made his debut with the club as a starter in a 3–1 home win game against Alanyaspor. On 18 May 2018, in the last matchday of the season he scored his first goal with the club in a 3–2 home win game against Antalyaspor.
On July of 2020, Villafanez returned to the Greek giants Panathinaikos F.C. with a 1+1 year loan deal from Monarcas Morelia.
Greek Passport
In 2014, Lucas started the procedure in order to claim the Greek citizenship, due to his great-grandfather who was from Piraeus, in order to be eligible for the Greek national football team. In December 2017, he was in the final stages for acquiring the citizenship and will be available for the Greek national football team, but coach Michael Skibbe has not confirmed if he will call-up Villafañez.
