It is perfectly normal for any plant that has been living indoors to find the great outdoors a bit of a challenge for its first days outside. Most of the damage seen your pictures are mechanical in nature where the wind has indeed bent the petioles but give your citrus tree more time outdoors and it should use the extra light and air to strengthen its shoot structure and reward you with a more resilient structure.
Bear in mind that the light levels outdoors can be 100 to 1000 times more than you get indoors even through a south facing window and if you let it adjust carefully over the next few days, it will quickly adjust to what must be better for it outdoors.
It is a little like taking the stabiliser wheels off your kid's bicycle. At first the kid will wobble and fall off a bit but very soon she or he will be cycling faster and be more daring than with the stabilisers.
I was faced with a similar challenge yesterday and after I brought home a plant rescue that has infected my monsteras with thrips and I had to take them outside and treat them with pesticide in order to protect my aquarium fish and shrimp. The plants are going to look worse before they get better but I hope the return of fragile British summer temperatures this week will ultimately give them sufficient boost to help them get over those pesky pests.
So, nothing to worry about regarding your lemon tree. Losing a few leaves is no big deal and will not affect the well-being of your tree. You are wise to leave it in some half shade for the next few days and even in half shade it will probably be getting more sunlight than indoors.
Trees really DO need to be outdoors for them to thrive but in your case, so long as frosts are not imminent of course. When you take your tree indoors again in early Autumnn, it will be much more sturdy but in the meantime, I hope you have the pleasure of seeing some fruit this summer.
