Move the outer key inward in an association

Here's an approach using @@@ (Apply at level {1}):

Prepend[#2, "Event" -> #] & @@@ lst
(* {
    <|"Event" -> 15000001, "Loss" -> 2.85396*10^8, "Exposure" -> 6.61052*10^10|>, 
    <|"Event" -> 15000002, "Loss" -> 1.25297*10^8, "Exposure" -> 1.57863*10^11|>,
    <|"Event" -> 15000003, "Loss" -> 2.05979*10^8, "Exposure" -> 6.88024*10^10|>
   } *)

As noted by @WReach in the comments, we can also use the (undocumented?) fact that associations behave as if they had the Flat attribute (meaning that e.g. <|a->1,<|b->2|>|> evaluates to <|a->1,b->2|>):

<| "Event" -> #, #2 |> & @@@ lst
(* same output *)

Join @@ KeyValueMap[Prepend[#2, "Event" -> #]&] /@ (Association /@ lst)

{<|"Event" -> 15000001, "Loss" -> 2.85396*10^8, "Exposure" -> 6.61052*10^10|>,
<|"Event" -> 15000002, "Loss" -> 1.25297*10^8, "Exposure" -> 1.57863*10^11|>,
<|"Event" -> 15000003, "Loss" -> 2.05979*10^8, "Exposure" -> 6.88024*10^10|>}

Alternatively, use Replace:

Replace[lst, HoldPattern[a_ -> <|b___|>] :> <|"Event" -> a, b|>, All]

same result

Using keyPush by @alancalvitti

keyPush[newKey_][<|k_ -> as_Association|>] := Prepend[newKey -> k][as];

keyPush["Event"][Association@#] & /@ lst

{<|"Event" -> 15000001, "Loss" -> 2.85396*10^8, "Exposure" -> 6.61052*10^10|>, <|"Event" -> 15000002, "Loss" -> 1.25297*10^8, "Exposure" -> 1.57863*10^11|>, <|"Event" -> 15000003, "Loss" -> 2.05979*10^8, "Exposure" -> 6.88024*10^10|>}