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Thanks for sharing the reproduction.

The problem is that the toString() implementation of the lambda ::requestLoad will reflectively lookup the method invoked by the lambda. This happens in the implementation of kotlin.jvm.internal.FunctionReference.toString(), which also explains why this method shows up in the stack trace:

kotlin.NotImplementedError: Function 'requestLoad' (JVM signature: requestLoad(Ljava/lang/Integer;)V) not resolved in class net.kusik.r8funrefissue.LazyListPaging: no members found
	at kotlin.reflect.jvm.internal.KTypeImpl$$Lambda$1.invoke(SourceFile:1297)
	at kotlin.reflect.jvm.internal.ReflectProperties$LazySoftVal.invoke(SourceFile:19)
	at kotlin.reflect.jvm.internal.KFunctionImpl.getDescriptor(SourceFile:3)
	at kotlin.reflect.jvm.internal.KFunctionImpl.toString(SourceFile:3)
	at kotlin.jvm.internal.FunctionReference.toString(SourceFile:7)
	at java.lang.String.valueOf(String.java:2924)
	at java.lang.StringBuilder.append(StringBuilder.java:132)
	at net.kusik.r8funrefissue.Snapshot.toString(Unknown Source:19)
	at java.lang.String.valueOf(String.java:2924)
	at net.kusik.r8funrefissue.MainActivity$onCreate$1$1$1.invoke(SourceFile:59)

The method called by the lambda is LazyListPaging.requestLoad(Integer). This method is only called from LazyListPaging.access$requestLoad(LazyListPaging, Integer), which is only called from LazyListPaging$snapshot$1.invoke(Integer). Therefore, the two requestLoad methods are inlined by R8 into the invoke method (after which they are removed, since there are no more calls to them). The problem now arises since the toString() implementation reflectively looks up the requestLoad method. In order for this to succeed, the method must be kept:

-keepclassmembers class net.kusik.r8funrefissue.LazyListPaging {
  private void requestLoad(java.lang.Integer);
}

The constructor of the kotlinc generated lambda looks as follows. In principle it would be possible to model in R8 that FunctionReference will reflect on the method specified by the arguments. This way R8 could in principle automatically synthesize the about rule. However, this would likely have a significant negative impact on code size (e.g., it would prohibit requestLoad from being eliminated), so I don't see us pursuing this idea, unless this would only apply to certain opt-in lambdas.

.method public constructor <init>(Ljava/lang/Object;)V
    .locals 7
    const/4 v1, 0x1
    const-class v3, Lnet/kusik/r8funrefissue/LazyListPaging;
    const-string v4, "requestLoad"
    const-string v5, "requestLoad(Ljava/lang/Integer;)V"
    const/4 v6, 0x0
    move-object v0, p0
    move-object v2, p1
    invoke-direct/range {v0 .. v6}, Lkotlin/jvm/internal/FunctionReference;-><init>(ILjava/lang/Object;Ljava/lang/Class;Ljava/lang/String;Ljava/lang/String;I)V
    return-void
.end method

From a code size perspective, it is also quite wasteful to store the strings "requestLoad" and "requestLoad(Ljava/lang/Integer;)V" on the lambda instance when they are unused. Ideally this would be optimized better.