The tight end earned second-team All-Pac-12 honors last season after catching 53 passes for 872 yards and a team-high 10 touchdown receptions.
The quarterback became last season the third quarterback in FBS history with 4,000 passing yards and 40 touchdown passes in consecutive seasons.
Dolphins send cornerback to the Cleveland Browns in a deal that involved a swap of seventh-round picks.
Lucas finished his Penn State career with 180 tackles, three interceptions and four sacks.
Grant, a 5-foot-6, 165-pound speedster, set a school record with four career kickoff returns for touchdowns. Two of those came in 2015.
In addition to liking the prospects the Dolphins landed, the Dolphins owner was pleased with the teamwork involved in making those picks.
The selection of cornerback Xavien Howard in the second round along with running back Kenyon Drake and receiver Leonte Carroo in the third round filled some needs and showed a willingness to be bold by moving up two different times.
The wide receiver had 29 touchdown catches at Rutgers, all of them coming over the past three seasons.
The running back's best season at Alabama came in 2013 when he rushed for 694 yards with eight touchdowns and a 7.5 average.
NFL.com’s draft bio compared the former Baylor cornerback to new Dolphins corner Byron Maxwell.
See exclusive images as the Dolphins were on the field for the second day of voluntary minicamp practices.
The non-contact practice, which featured some 7-on-7 and team drills, was Head Coach Adam Gase's first opportunity to get an up-close look at his new players.
Get an AFC East report on the New England Patriots as lead writer for Dolphins.com Alain Poupart and Ben Volin of The Boston Globe discuss the state of the Patriots this offseason.
Get an AFC East report on the New York Jets as lead writer for Dolphins.com Alain Poupart and Dan Leberfeld from jetsconfidential.com discuss the state of the Jets this offseason.
Get an AFC East report on the Buffalo Bills as lead writer for Dolphins.com Alain Poupart and Bills Insider and lead journalist from Buffalobills.com Chris Brown discuss the state of the Bills this offseason.
Ride along as Sam Madison interviews Mike Pouncey.
View photos of Dolphins players as they participate in the first day of the team's 2016 Offseason Program.
View photos of Dolphins players as they arrive at the Doctors Hospital Training Facility for the beginning of the team's 2016 Offseason Program.
View the latest images from the second phase of the stadium modernization efforts taking place this off-season.
See images of the new Dolphins cornerback throughout his NFL career.