The Spanish champions hold a 3-0 aggregate lead ahead of Thursday's match after a hard-fought away win earlier this month.
L'Hospitalet, who sit 11th in the regonialised third tier of Spanish football, put up a good fight on that occasion - the game still goalless after an hour.
It was the introduction of France international Antoine Griezmann that changed the game, though, as he eventually broke the deadlock.
Further goals for Gabi - from the penalty spot - and Cristian Rodriguez in the last 10 minutes virtually sealed Atleti's place in the last 16.
Those late strikes mean Simeone can give his squad a chance to rest, particularly after Sunday's disappointing 1-0 home defeat to Villarreal.
Atleti slipped seven points behind La Liga leaders and city rivals Real Madrid with the loss, which came due to Luciano Vietto's 84th-minute strike for the visitors.
Diego Simeone' side, who drew Bayer Leverkusen in the last 16 of the UEFA Champions League on Monday, missed a host of chances in that match, and the coach hinted at changes when five players from Atletico's reserve team took part in a full training session at the start of the week.
Carlos Ramos, Borja Martinez, Nacho Monsalve, Ivan Perez and Sekou Keita may all come into contention for the hosts.
Atleti, 10-time winners of the competition, will be looking to bounce back from last season's semi-final defeat to eventual champions Real Madrid.
The home side, who last won the Copa del Rey in 2013, were beaten 5-0 on aggregate by Real on that occasion.
L'Hospitalet enter the match on the back of two wins - with a 2-0 triumph against Eldense on Sunday giving them momentum.
Midfielder Ruben Alcaraz scored in that success and with three goals in his last five matches, represents a threat to Atleti.
Alcaraz also scored in L'Hospitalet's 3-2 win over Izarra earlier in this season's competition.
The hosts will also be tested by 24-year-old striker David Haro, who has eight league goals for L'Hospitalet this season, including four in as many matches.
