This is going to be a bit of a long post as I have a bunch of different Lions sets.
The first cards I have I believe were sold around 1989. These are laminated photo cards. Jay Shelton has mentioned to me (and sent me a scan) of some kind of similar Giants cards from roughly the same time frame so this might be a common type of team collectible from that era:
I have seven of these - Koji Akiyama, Kazuhiro Kiyohara (2 different), Kimiyasu Kudoh, Hisanobu Watanabe (3 different). The cards are a little bigger than normal.
This is a set of 22 postcards featuring 23 players from the 1990 Lions:
The cards are unnumbered other than uniform number. The players are Koji Akiyama (#1), Haruki Yoshitake (#2), Kazuhiro Kiyohara (#3), Seiji Tomashino (#4), Hatsuhiko Tsuji (#5), Norio Tanabe (#6), Hiromichi Ishige (#7), Tadakatsu Hanyuda (#10), Takehiro Ishii (#11), Hirohisa Matsunuma (#15), Taigen Kaku (#18), Tomio Watanabe (#21), Ken Hirano (#24), Yoshitaka Katori (#26), Tsutomu Itoh (#27), Ty Van Burkleo (#29), Ryoji Moriyama (#31), Orestes Destrade (#39), Hisanobu Watanabe (#41), Kazuhito Nishimoto (#42), and Kimiyasu Kudoh (#47) plus a postcard featuring both Tetsuya Shiozaki (#16) and Tetsu Suzuki (#34).
1999 "Hit! Foot! Get!"
I don't know if this card was part of an actual set or just some sort of promotional card for the Lions. It appears to be related somehow to the opening of the Seibu Dome (the ballpark opened in 1979 but didn't have a roof on it until 1999).
2001 Fan Club Cards
As Jason points out, a lot of the Lions cards between 2001 and 2007 (if not more) have multiple designs per set so it's difficult to figure out which sets a card comes from unless you can see the back of it. For the 2001 set, I have the same four cards that Jason lists - Kazuo Matsui (#7), Ken Suzuki (#8), Taisei Takagi (#10) and Tsutomu Itoh (#27):
2004 Original Player Cards
While this set still has multiple designs, it looks like at least some of the cards use the same design. Jason actually has six cards listed for this set but I only have three of them.
2006 Original Player Card
This set is ridiculous. I have 34 of these cards and it looks like every one of them have a different design!
The 34 cards I have are: Koki Fujiwara (#63), Mitsutaka Gotoh (#41), Taketoshi Gotoh (#6), Hidekazu Hoshi (#61), Tomoki Hoshino (#26), Masahide Kaizuka (#39), Takahiro Matsukawa (#48), Hironori Matsunaga (#24), Kenta Matsusaka (#58), Akira Miyakoshi (#66), Kazuaki Miyazaki (#43), Keisuke Mizuta (#45), Junji Nishikawa (#38), Kohsuke Noda (#22), Kohji Ohnuna (#15), Atsushi Okamoto (#28), Goh Ono (#67), Tomoaki Satoh (#10), Hiroyuki Shibata (#2), Takumi Shiigi (#55), Eiji Shotsy (#25), Haruki Sugiyama (#62), Kohji Tahara (#68), Hiroyuki Takagi (#4), Fumikazu Takanami (#0), Hisashi Takayama (#44), Yasuhiro Tanaka (#57), Masahiro Tazaki (#35), Yuya Tazawa (#50), Tatsuyuki Uemoto (#49), Minoru Yamagishi (#36), Ayumu Yamamoto (#59), Satoshi Yamazaki (#17) and Taichi Yoshimi (#31).
2008 Fan Club
Jason has a bunch of information on this set. All the cards appear to have the same design but a different border color. Jason says there are at least five different border colors - grey, white, green, blue and red and that apparently the blue border cards were "replacement cards" when the initial batch of a player's cards ran out. I will amend that statement by saying there are actually two different shades of blue for border color - I suspect that the darker blue bordered cards are the "replacement" cards as the one I have of Takayuki Kishi doesn't have a number on the back.
Jason has a lot of these listed but I have a couple that he doesn't have the numbers for - Hisashi Takayama (#26), Takatoshi Gotoh (#29) and Yutaro Ohsaki (#31). Note that the cards have actual numbers on the back and aren't simply numbered by uniform number.
2009 Fan Club(?)
Not much to say about these. Jason lists five of these cards which cover the four I have:
2011 Fan Club(?)
Again, I don't have much to say about this set. Jason lists about 30 cards or so from this set, including the four I have.
I have representatives from possibly two separate sets from 2013. Jason has a listing of 15 cards from the first of these, but oddly enough he doesn't have any of the five cards I have - Takumi Kuriyama (#1), Tatsuya Ohishi (#15), Yusei Kikuchi (#17), Shogo Akiyama (#55) and Takeya Nakamura (#60).
I have four cards from the other set which Jason doesn't have a listing for - Takumi Kuriyama (#1), Yusei Kikuchi (#17), Hideto Asamusa (#32) and Shogo Akiyama (#55):
I've got representatives from three separate Fanclub sets from 2014. The front design of each set are all similar but I don't think these are parallel issues. I have three cards from the first set (which Jason does not have listed) - Takumi Kuriyama (#1), Takayuki Kishi (#11) and Hideto Asamura (#32):
I have nine cards from a gold bordered set (the same nine cards that Jason has listed):
And I have 11 cards from a silver bordered set (and again it's the same group of cards that Jason has listed):
It probably doesn't mean anything, but I noticed that there's no overlap in players in the (possibly) small sample size of 2014 cards I have. It's possible that the Lions essentially issued these in series with a third of the team in each set. But that's purely speculation on my part.
Finally I have eight cards from a set released this season - Takumi Kuriyama (#1), Ryota Wakiya (#7), Naoto Watanabe (#8), Yutaro Osaki (#9), Fumiya Nishiguchi (#13), Ryoma Nogami (#20), Ken Togame (#21) and Hideto Asamura (#32):
I found a tiny bit of information on this set on the Lions fan club's website, basically that the cards are given away to fan club members at home games.