I will note that you have to carry your bags yourself between the two airports. Some people aren't aware of this.

Your success will depend on your immigration status coming in to the UK (EU lines are usually quicker than non-EU), what time bag-drop closes for your LGW-LAS flight (assuming you check-in online beforehand; for most airlines it is 45 minutes) and traffic (since there isn't a direct rail link, you are at the mercy of the M25).

The best way of making this connection would be to travel hand baggage only to save a bit of time on arrival and again at check-in (since if you travel HBO, check in online and print your boarding pass before you leave you can head straight through security at LGW - there is no formal conformance time).