I spent forever trying to get my controller to work. It is just a generic one. Nothing worked. None of the mappers worked for me. I hope I can post this here, but this guy's solve was easy and worked perfectly. If you are going crazy trying to get your controller to work, do what this guy says to do. EDIT: I also had to map the other buttons as well, since Lara stopped grabbing and swimming. After I mapped those, the gamepad works perfectly.

Tomb Raider I: XBOX/Playstation Controller Fix
The following are steps to go about tweeking the DosBox mapper for PC controllers. This was tested on a Logitech F710 which has X-input/'XBOX' and D-input/'Playstation' modes. I will be posting controller instructions to the other classic TR games(TR 2-6) for those with this gamepad in the respective forums when I get the time.(Note: Legend, Anniversary and Underworld natively support XBOX controllers.)

In thoery, this fix should work with any controller as long as your PC recognizes it.

Note for XBOX 360 Controller Users: The following link is a streamlined guide courtesy of Darth Sidious [PT]

Tomb Raider I Xbox 360 Controller Support
A Guide for Tomb Raider I
By: Darth Sidious [PT]
Basically, this is an easy way of playing Tomb Raider 1 with an Xbox 360 controller.

Steps to take:
1. If you have already modified the mapping ingame reset the keys to their original settings with the exception of the Jump, Roll, Action and Draw Weapon commands. Map these 4 commands to the desired gamepad buttons.

User Keys settings before partial gamepad configuration.(Visual aid for Tomb Raider I: XBOX/Playstation Controller Fix post in forums.)
A Screenshot of Tomb Raider I
By: CrimsonBlitz

Your ingame mapping should look something like this...
------------------------User Keys-----------------------------------
PAD8 Run_____________PAD+ Jump(Change to desired button)
PAD2 Back____________ENTER Action(Change to desired button)
PAD4 Left_____________PAD3 Draw Weapon(Change to desired button)
PAD6 Right____________PAD0 Look
PAD7 Step Left_________PAD5 Roll(Change to desired button)
PAD9 Step Right
PAD1 Walk____________PAD. Inventory

User Keys settings after partial gamepad configuration.(Visual aid for Tomb Raider I: XBOX/Playstation Controller Fix post in forums.)
A Screenshot of Tomb Raider I
By: CrimsonBlitz

Note: The Action command will also double as a menu selection key.

The game will natively detect directional functions on the gamepad.

2. Close the game.

3. Relaunch the game. When the game starts to load you'll see the DosBox logo leading to a classic DOS loading screen. On that screen hit ALT+ENTER. This will window your game. Immediately after its windowed hit CTRL+F1 to get to the DosBox mapper. It takes a little practice to get to it as at times it may crash. Try not to move the mouse or click anything during this phase as it will crash you.

4. Once you're in the mapper you are going to want to modify keys according to the "Default Keys" you saw ingame earlier. These are the keys you want to modify...

DEL Step Right
PGDN Step Left
SHIFT Walk
PAD0 Look (PAD0 is 0 on number pad)
ESC Inventory(acts as a pause/continue/cancel/skip scene)

Default Keys settings.(Visual aid for DosBox mapper. See Tomb Raider I: XBOX/Playstation Controller Fix post in forum.)
A Screenshot of Tomb Raider I
By: CrimsonBlitz

Highlight one of these keys on the mapper with your mouse. Once highlighted you'll notice an "Add" button appear near the bottom of the mapper. Click "Add" then press the desired button for that command on the gamepad. Repeat this process for the remaining 4 commands above. After you modified 2-3 keys save but -don't- exit. The mapper will somrtimes forget an input and you will have to re-enter so be patient.

Note: The mapper will not let you assign duplicate keys with the same command and there is no need to. Example, you need only modify -one- Shift key.

5. Verify that the 5 keys listed above are mapped by clicking on them in the mapper and seeing the gamepad command applied to the key on the left side of the mapper. Once verified hit Save then Exit.

Enjoy, you now have full controller support for TR1!