Yes and no. They don't need a lot and their first XI would be very difficult to improve. Their goalkeeping and defense is set. Midfield is set, especially with a full season of Chamberlain. Forwards we have known they are very high on Brewster and want to give him a chance (rightfully or wrongfully). I think there is a hole for Mane cover (left sided forward) but it honestly it may be easier said than done to bring in a player who knows that there aren't a ton of minutes to be had necessarily. That (and backup left back, which has the same issue) are the areas that are missing.
While it's nice Liverpool don't want to block their young players, there are a lot more games on the calendar this season following a summer on Copa America and AFCON. Also, Liverpool isn't trying to get 4th in the league anymore. They are trying to get 1st, and have to defend the Champions League. They have proven me wrong before but their depth could be an issue. I think a guy like Lozano to cover Mane would make a ton of sense, and he wouldn't cost the moon, especially in this market, if you could get him for around 30m.
I mean Tottenham just signed Jack Clarke for cover - could Liverpool look for a similar profile there? Liverpool wanted Lloyd Kelly as backup LB, but Kelly chose more minutes at Bournemouth, which you can't really fault him for. Those caliber players is probably where Liverpool will be shopping in. Young, projectable, possibly homegrown cover. That being said, Liverpool are two deep in every position, but you'd wish there was a little more quality up front. I think they may give Brewster a chance to handle it in 2019, and could look to make a forward purchase in January if it hasn't worked out; but they clearly want to give Brewster a shot. Problem is league could be gone by then.