What is the recommended range for the number of players in Liar Dice?
There's no clear consensus on recommended player count

As you're not playing an official version of liar's dice, giving you a hard and fast rule for your own game, would be guesswork. What follows deals with the 'official' version of the game - a perspective which you said might also be useful.

On the website boardgamegeek, on each game listing, users are able to vote on the player counts at which they would recommend playing a particular game. For each possible 'player count' users are able to select either 'Not recommended', 'Recommended' or 'Best'.
The community's recommendations for Perudo (an alternative name for Liar's Dice), based on 166 respondants, are as follows:

More than 50% of users think Perudo is 'Best' with 5 / 6 players
57% of users would at least 'Recommend' playing Perudo with more than 6 players (42% would not recommend it)

I'm not sure you need to worry, based on your criteria
You stated that one of your concerns about high player counts was: 'the dice would never reach the 8th player because the escalating hands would be too hard to beat'.
In most common variants of liar's dice this isn't an issue becuase play is circular rather than linear. Whenever one hand is finished the next hand resumes from that point in the circle, rather than starting back with the original first player. So, if a 'hand' resolves before some players have participated, those same players will be among the first players to participate in the next 'hand'.
However, adding extra players will make the game longer

The total play time will be longer

Liar's dice is commonly a player elimination game - the more players there are to eliminate the longer it will take to reach its conclusion. As you intend this to be a light filler that's probably not desirable.
This is less of an issue if you're not concerned with playing the game to completion.

Time between a player's turns will increase

If this is a filler to keep people engaged between other games, then a longer time between player's turns is not ideal. that said, in my experience of Liar's Dice, players's do tend to remain fairly invested in paying attention to other player's turns, in comparison to some other games.

Time spent while eliminated will increase

As mentioned above, Liar's Dice is most commonly a game that involves player elimination (on BGG 'Player Elimination' is listed with 'Dice Rolling' and 'Betting/Wagering' as one of the game's key mechanisms). In an eight player game the first player to get eliminated could conceivably spend significantly longer not playing the game, than they ever did playing it. Once again this probably isn't that desirable for a filler.
How much weight should be put on any of these factors is up to you. You know your context, you know your players and most importantly, you know the exact rules of the specific Liar's Dice variant your playing.
If on reflection you do decide that player count is a concern, then one way that these issues could be avoided / mitigated is by splitting larger groups into separate games.