You could store your events in a DynamoDB table keyed at a UUID, and have a hash-range schema GSI on this table where the hash key would be an expiry time bucket, like the hour an event expires, 20150701T04Z, and the range key of the GSI could be the exact timestamp (unix time). That way, for a given hour-expiry bucket, you can use a range Query on the hour you are expiring events for, and take advantage of key conditions to limit your read to the time range you are interested in. GSI do not enforce uniqueness, so you are still OK even if there are multiple events at the same Unix time. By projecting ALL attributes instead of KEYS_ONLY or INCLUDE, you can drive your event expiry off the GSI, without a second read to the base table. By adjusting the size of your expiry buckets (hours or minutes or days are all good candidates), you can greatly reduce the chances that your writes to the base table and queries on the GSI do not get throttled, as the expiry buckets, having different hash keys, will be evenly distributed throughout the hash key space.
Regarding event processing and the use of Lambda, first, you could have an EC2 instance perform the queries and delete items from the event table as they expire (or tombstone them by marking them as expired). Deleting the event items will keep the size of your table manageable and help you avoid IOPS dilution in the partitions of your table. If the number of items grows without bound, then your table's partitions will keep splitting resulting in smaller and smaller amounts of provisioned throughput on each partition, unless you up-provision your table. Next in the pipeline, you could enable a DynamoDB stream on the event table with the stream view type that includes old and new images. Then, you could attach a Lambda function to your Stream that does the event-driven processing (push notifications, etc). You can have your Lambda function fire notifications when old is populated and new is null, or when the difference between old and new image indicates that an event was tombstoned.