1) Give Rajai Davis Everyday At-Bats
This would usually be the default option when two players are in a time-share situation, that you would rely more heavily on the other player. Unfortunately, Davis was signed specifically because he would work out best in a platoon setup.
However, the discrepancy for Davis between hitting against lefties and hitting against righties is huge. Against lefties for his career, he walks 8% of the time, hits for respectable power (.13 ISO) with 40 more points in his average, resulting in a .343 wOBA. On the other hand, he only walks 4% against righties, his ISO is under .1, which all comes together to present a career .288 wOBA – basically making him worse than a replacement player in those situations.
The Tigers could look to give Davis AB's selectively against right-handers, perhaps those that he's shown particular success against, but they'd likely be setting themselves up for failure if they plan to just use Davis on a daily basis in left.
As a switch-hitter and left-handed hitter, respectively, and with some background playing left field, both could theoretically fill the spot that was opened up by the injury to Andy Dirks.
While Kelly was a favorite of Jim Leyland's, his historical performance against right-handers isn't that strong, even though it's better than his lefty/lefty splits. He hits just .235 against lefties with a .292 wOBA, making him only marginally better than Davis. Having him already in the game on a regular basis also potentially limits his versatility value, a key component of what he brings.
Much like Kelly, Lombardozzi's potential is pretty limited. For starters, the Tigers have been having him focus his time on working in the middle infield to be a capable backup for Jose Iglesias, in addition to Ian Kinsler. Asking him to play double duty just puts more stress on a limited use bench player. In addition, offensively, he's in the same category – career .289 wOBA against right-handed pitching with a .269 average. So, Lombardozzi could bring his gritty style and a rather empty average to the slot, making him a rather undesirable option, as well.
The cast of players the Tigers could potentially rely on is mostly made up of non-roster invitees, along with Fields, who was recently added to the 40-man roster. Collins, like Fields, spent 2013 in Double-A Erie. Carrera and Crowe were both signed as minor league free agents, with the intent of providing depth to the upper levels of the farm system.
Carrera is the player that will probably get the first extensive look. He was a solid part-time player for two years in Cleveland in 2011 and 2012. He only has a few hundred career big league at-bats, but in that time, his AB's against right-handers are still no better than what we've seen out of everyone else - .255 average, wOBA of .291. He has been a threat on the base paths, but it's unlikely he'd be a better one than Davis would already be.
Trevor Crowe is a switch-hitter that has gotten most of his time from the left side of the plate against right-handed pitching. He's struggled even more than the other options, with just a .279 wOBA, making it unlikely he'd beat out the internal options and Carrera to earn playing time.
The final two come down to a pair of prospects that maintain big league potential, but might not be developed enough to be ready for consistent playing time in Detroit, at least not right out of the gate. Both hit from the left side which is an initial plus, but neither were even able to post an .800 OPS in a hitter-friendly park for Erie. Needless to say, they might be good options to be a platoon player in Detroit in left field SOME day, but that day is probably not today (or tomorrow).
The summary is that there's simply no good internal option. Every single one in fact would likely post a wOBA under .300 over an extended period of time, unless one of the two prospects comes on strong this spring and emerges as a worthy complement.
The Tigers are fine to have an open tryout and leave the position to be determined for the next few weeks, but it'd be advisable for them to start searching the waiver wire as we get later into spring training to see if a player that might fit gets put on the market or becomes available via trade. Given that this isn't simply a short term thing that the Tigers will need to make due on for a couple weeks of games, it warrants serious consideration to make a move.
In the event they don't, the final spot on the roster suddenly becomes a much more open competition, including a number of the outfielders mentioned above, along with infielders Danny Worth and Hernan Perez, either of whom could serve a valuable bench role and allow for Kelly and Lombardozzi to get more work in elsewhere, including left field.