TLDR: In your specific case, Lizardfolk are from Volo's Guide To Monsters, a book that is not allowed in DDAL Eberron play, and it did not start the Eberron Campaign at level 1. It is not a legal character for Oracle of War Eberron DDAL play.
They are entirely separate campaigns.
DDAL's Forgotten Realms campaign and DDAL's Eberron campaign have different character creation rules and different character advancement rules. They are incompatible.
Character Creation is Different
From the Oracle of War Player's Guide v1.3 in the D&D Adventurers League Player & DM Pack. The first line (emphasis added) makes it clear Eberron characters are campaign-specific; even characters from the previous Eberron campaign are incompatible with the current Oracle of War campaign.
You’ll need an Eberron character made specifically for the D&D Adventurers League Oracle of War campaign. Characters from the Embers of the Last War campaign cannot be used, although they can be recreated starting at 1st level using the rules of the Oracle of War campaign. All Eberron characters begin at 1st level, unless you possess campaign documentation that states otherwise or further rules countermand this.
STEP 1: CHOOSE A RACE AND CLASS
Oracle of War characters can choose race and class options from the Player’s Handbook, Xanathar’s Guide to Everything, and the Eberron: Rising from the Last War campaign sourcebook only (unless you possess campaign documentation providing additional options).
You may select the Variant Human Traits option from the Player’s Handbook.
The AL Players Guide v9.2 - Forgotten Realms in the same D&D Adventurers League Player & DM Pack has different rules.
You’ll also need a character made for the D&D Adventurers League. All characters begin at 1st level.
STEP 1: CHOOSE A RACE AND CLASS
Forgotten Realms characters can choose race and class options from the Player’s Handbook and one other resource—a rule called “PHB+1.” Additional resources include the following products:
I won't bother going into detail on the PHB+1 rule, it's been covered to death here. While there is sufficient overlap in the range of permitted books for one to create a level 1 character that satisfies both sets of rules, the requirement to start at level 1 combined with the Eberron requirement to be created exclusively for the campaign makes the characters incompatible.
Advancement is Different
From the Oracle of War Player's Guide v1.3 in the D&D Adventurers League Player & DM Pack:
In the Oracle of War campaign, your character advances one level at the end of each adventure, unless it is a special event, for which level advancement is optional. Your DM tells you when you’ve gained a level, and when level advancement is optional.
In Eberron DDAL play, advancement is controlled by the content you play - if you play, you must advance when indicated. The exceptions are explicitly spelled out in the individual modules.
From the AL Players Guide v9.2 - Forgotten Realms in the same D&D Adventurers League Player & DM Pack:
Your character gains a level upon completing an adventure. In hardcover adventure sessions, your DM will tell you when you’ve gained a level. Otherwise if, after four hours of play (or eight hours at tiers 2 – 4) in a hardcover adventure, your DM doesn’t tell you that you’ve gained a level, you gain a level. In this instance your character advances to the next level at the end of the session.
If you’d like to continue playing at your current level, you can decline to gain a level, although it has an impact on other rewards that you receive.
In FR DDAL play, advancement is effectively player controlled. During a hardcover session, the DM can trigger advancement earlier than 8 hours of play (4 in tier 1), but they can't prevent1 a character from advancing at the listed pace. The player, on the other hand, has the choice - a player could choose to have a character perpetually in a choose tier by simply ceasing advancement. Eventually they'll run out of money and downtime (the "impact on other rewards" mentioned above), but it's an option for a Forgotten Realms character.
1They can ask and encourage not to, but their only real control is refusing to allow the character at the table.