LC: GoL is a much more arcade-like game than many of the others in the Tomb Raider franchise, but it is no less fun to play.
The story follows Lara and Totec as they attempt to prevent Xolotl from destroying the world. The story is told through various means within the game, from narration at the start to comic and "live" cutscenes. This could have possibly been made more consistent throughout, but in no way affects the quality of the story. It does at times seem like many of the classic villain tropes come through in Xolotl however: Manic laughter, taunting the player etc., but this isn't too over the top.
The gameplay has 2 main styles: linear and open levels. The linear levels (usually in tombs) generally require fighting your way through monsters, solving puzzles with balls and hazards like spike pits and fire, and jumping puzzles. The open levels are similar in what they require from the player, but instead of funneling you through a tomb you are generally given a "hub", with multiple paths to tombs to "complete". You need to do all of them anyway, so it's sort of the illusion of an open level more than anything.
The puzzles themselves are generally quite easy, although there are one or two of the jumping puzzles which, like in all games, can be a bit frustrating. Overall, though, for an arcade-level game they are well made. The fighting scenes, which can occur randomly at any time (monsters spawn from out of the ground), seem to result in a sort of pseudo-bullet-hell type gameplay, which isn't a bad thing. The game difficulty can be changed depending on how you like your fight scenes (easy being you just tear through enemies, and hard gives you enemies that soak up bullets).
To aid the fight mechanic you can collect different weapons (machine guns to explosive grenades), powerups (health boosts etc.) and various relics. The relics require a charge which when filled can enhance your fighting power. At the endgame, when the top tier ones are unlocked it becomes very easy to fight through vast numbers of enemies, which the game will happily provide.
The sound design is very good in this game, with dramatic music when required and more ambient music for within non-combat puzzle areas. Similarly, the voice acting is very good, even if it is only heard in cutscenes. Given the isometric-style view of the game, you never really see things in a close detail, but even at a distance the graphics in this game are very nice, from the rocky textures of walls and brickwork to the design of the monsters and characters you fight.
The game plays either using a controller or a keyboard. Personally, I would just stick to using a controller, if you have one, as the arcade-like nature of the game suits this playstyle best.
In terms of bugs: If you intend to use a controller, note that the game might not automatically assign it to player 1, so you may need to go into the options to manually assign it. I only had the game crash catastrophically once. No idea why it happened, but restarting it solved the issue.
To summarise: If you want a more laid-back adventure game, then this is definitely worth buying. It isn't terribly difficult, but it does offer a nice story and nice gameplay.