Yes, Lara Croft is very rich due to inheritance from her parents.
She was born into a rich and noble English family, gamers who have played the first games will have noticed this while they are going around the massive mansion that she calls home. However she eventually loses contact with her family, there are different versions of the stories due to there being more than one reincarnation of the Tomb Raider story. In one account her parents disown her in the other her parents are killed in a tragic accident (Lara is still trying to uncover the truth of what has happened to her parents to this day, despite the dozen games created this question has yet not been fully answered). Regardless Lara Croft has chosen the life of adventure and helping the world over a life of luxury and comfort.
Furthermore, Lara Croft handles priceless artifacts which she sells to museums, galleries and private collectors who are willing to pay a lot for this kind of items. This allows Lara to buy all her expensive equipment from speedboats, diving equipment, and her infinite ammo. Furthermore, Lara has a lot of sidekicks and assistants throughout her adventures and it is not 100% if they are funded by her or by archaeological organizations.Her father was also a well-known archaeologist who made significant discoveries and money from this, which earned him the title of Lord making him Lord Richard Croft and therefore making him a powerful and wealthy figure.