You should reconsider a travel to Tibet if you suffer from heart or any cardiac as well as respiratory problems, in any case get advice from you doctor at home!
Most foreigners, as well as most Chinese, when arrive in Lhasa, suffer from high altitude sickness symptoms immediately! You might get disturbed with a slight to even strong headache, maybe lying on bed for one/two days! So be aware to consider AMS (Altitude Mountain Sickness) seriously.
Usually you suffer a slight headache and some sleeplessness during the first night. It's advisable take some mild medicine for headache and avoid drinking of any alcoholic drinks upon your arrival. Drink more water to help your body to acclimatize and don'tt be surprised if the first nights headache occurs.
The following precautions may help to keep AMS away from you:
Since fluid loss usually accompanies the acclimatization process, drink plenty of fluids (3 - 4 liters daily at least) and eat carbohydrate food to maintain properly health.
Do not over exert and maintain light activity right after your arrival.
Stay way from smoking and alcohol and other depressants such as tranquilizers and sleeping pills, which will depress the respiratory drive and oxygen intake.
Never go higher with symptoms of AMS
It is significant that you report any symptoms of AMS immediately to other group members in the trip.